A292993 Numbers n such that 15 applications of 'Reverse and Subtract' lead to n, whereas fewer than 15 applications do not lead to n.

10695314508256806604321090888649339244708568530399, 11787342277647023379656208735392766826312885522179, 14638655404662283607788118901219361883250644206458, 26730889210860738952361172793674105293199801097128

Offset

1,1

Comments

There are 15 fifty-digit terms in the sequence. Further terms are obtained (a) by inserting at the center of these terms either any number of 0's (for 10695314508256806604321090888649339244708568530399, 26730889210860738952361172793674105293199801097128, 29899105876561459824028272726867015583422139910097, 49102887245877091252834454555175879833145710289795, 55448121688278511195278554322651878413601497706634, 68315444154984874470735536347381553142144945548514, 88608272072487486790367718123691321620571972829202) or any number of 9's (for the other eight terms) and (b) by concatenating a term any number of times with itself and inserting an equal number of 0's at all junctures. Method (b) may be applied recursively to all terms. - Ray Chandler, Oct 15 2017

Links

Ray Chandler, Table of n, a(n) for n = 1..15

J. H. E. Cohn, Palindromic differences, Fibonacci Quart. 28 (1990), no. 2, 113-120.

Formula

n = f^15(n), n <> f^k(n) for k < 15, where f: x -> |x - reverse(x)|.

Example

10695314508256806604321090888649339244708568530399 -> 88608272072487486790367718123691321620571972829202 -> 68315444154984874470735536347381553142144945548514 -> 26730889210860738952361172793674105293199801097128 -> 55448121688278511195278554322651878413601497706634 -> 11787342277647023379656208735392766826312885522179 -> 85335216543715843349697571530304565248364338856532 -> 61769333197331586809394053950610230396629777603174 -> 14638655404662283607788118901219361883250644206458 -> 70821589200576532783422862287551276343389811477183 -> 32644177302242165567844635465112552775889512964376 -> 34702744296615559953311818179764003348330864180247 -> 39505402506768770093485363631571992203338380540496 -> 29899105876561459824028272726867015583422139910097 -> 49102887245877091252834454555175879833145710289795.

Crossrefs

Cf. A072142, A072143, A072718, A072719, A215669, A292634, A292635, A292846, A292856, A292857, A292858, A292859, A292992.

Sequence in context: A135956 A095490 A280419 * A095492 A095494 A246290

Adjacent sequences: A292990 A292991 A292992 * A292994 A292995 A292996

Keyword

nonn,base,changed

Author

Ray Chandler, Sep 28 2017

Status

approved