07-30-2015, 04:53 PM

Every natural number appears at some position in the concatenation of the natural numbers - sometimes called The Gods' Triangle, but let us call it N:

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500....

For example

399

starts at the

1087th

digit of N &

400

at the

1090th

digit, counting from the first 1 rightwards.

The programme for the 49G below gives the starting position in N for the entry integer.

Challenge

You will notice that for consecutive integers, eg 399 & 400, the positions are not consecutive, so 1088 & 1089 do not appear as the starting positions of any integer.

Write a programme that on input of the index of a number, say C, that cannot appear as position of any integer returns C, eg

for index

1

the programme returns

11

as 11 is the lowest number not representing the start position of an integer.

Clarification following posts #2 & #3

For input

2

the programme should return

13

for 3, 15........

Sorry for the imprecision of definition.

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500....

For example

399

starts at the

1087th

digit of N &

400

at the

1090th

digit, counting from the first 1 rightwards.

The programme for the 49G below gives the starting position in N for the entry integer.

Challenge

You will notice that for consecutive integers, eg 399 & 400, the positions are not consecutive, so 1088 & 1089 do not appear as the starting positions of any integer.

Write a programme that on input of the index of a number, say C, that cannot appear as position of any integer returns C, eg

for index

1

the programme returns

11

as 11 is the lowest number not representing the start position of an integer.

Clarification following posts #2 & #3

For input

2

the programme should return

13

for 3, 15........

Sorry for the imprecision of definition.

Code:

If you don'like CODE .... replace it with xSIZE COERCE.

::

CK1&Dispatch

# FF

::

FPTR2 ^ZABS

DUP

CODE 00025 143174E78FB9760131174143818F858DC7530

DUPUNROT

FPTR2 ^#>Z

FPTR2 ^RMULText

Z1_

FPTR2 ^RADDext

Z10_

ROT

FPTR2 ^PPow#

Z1_

FPTR2 ^RSUBext

Z9_

FPTR2 ^ZQUOText

FPTR2 ^RSUBext

;

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