A072718 -id:A072718 - cp's OEIS frontend

A292634 Numbers n such that 4 iterations of 'Reverse and Subtract' lead to n, whereas fewer than 4 iterations do not lead to n.

169140971830859028, 312535222687464777, 464929563535070436, 651817066348182933

Offset: 1

Meritxell Vila Miñana, Sep 20 2017

There are 4 eighteen-digit terms in the sequence. Terms of derived sequences can be obtained either by inserting at the center of their digits any number of 9's or by concatenating a term any number of times with itself and inserting an equal number of 0's at all junctures.

			|169140971830859028 - 820958038179041961| = 651817066348182933
|651817066348182933 - 339281843660718156| = 312535222687464777
|312535222687464777 - 777464786222535213| = 464929563535070436
|464929563535070436 - 634070535365929464| = 169140971830859028

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

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

n = f^4(n), n <> f^k(n) for k < 4, where f: x -> |x - reverse(x)|.

Terms ordered by Ray Chandler, Sep 27 2017

A292635 Numbers n such that 5 applications of "Reverse and Subtract" lead to n, whereas fewer than 5 applications do not lead to n.

Original entry on oeis.org

10591266563195008940873343680499, 27547681086656717245231891334328, 54795638726597554520436127340244, 68723845538328853127615446167114, 88817367774609971118263222539002

Offset: 1

Meritxell Vila Miñana, Sep 20 2017

There are 5 thirty-two-digit terms in the sequence. Further sequences can be obtained by inserting at the center of these terms any number of 9's and by concatenating a term any number of times with itself and inserting an equal number of 0's at all junctures.

			10591266563195008940873343680499 -> 88817367774609971118263222539002 -> 68723845538328853127615446167114 -> 27547681086656717245231891334328 -> 54795638726597554520436127340244 -> 10591266563195008940873343680499

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

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

n = f^5(n), n <> f^k(n) for k < 5, where f: x -> |x - reverse(x)|.

Terms ordered by Ray Chandler, Sep 27 2017

A073142 List of smallest solutions for some k of x = f^k(x), n <> f^j(n) for j < k, where f: m -> |m - reverse(m)|.

Original entry on oeis.org

0, 2178, 11436678, 108811891188, 118722683079

Offset: 1

Klaus Brockhaus, Jul 17 2002

In the definition, j can be restricted to proper divisors of k. A073143 gives the corresponding values of k. A073144(n) gives the smallest m such that the 'Reverse and Subtract' trajectory of m leads to a(n). Presumably a(6) = 1186781188132188 with k = 17.

			a(3) = 11436678 is the smallest solution of x = f^14(x) and there is no k such that x = f^k(x) has a smallest solution between a(2) = 2178 and a(3).

Cf. A072137, A072141, A072142, A072143, A072718, A072719, A073143, A073144.

Offset changed by N. J. A. Sloane, Dec 01 2007

A073143 Numbers k such that A073142(n) = f^k(A073142(n)), where f: m -> |m - reverse(m)|.

Original entry on oeis.org

1, 2, 14, 22, 12

Offset: 1

Klaus Brockhaus, Jul 17 2002

Presumably a(6) = 17. a(n) is the length of the periodic part (cf. A072137) of the trajectory of A073142(n). Question: Does every k > 0 appear in this sequence?

			a(3) = 14 since A073142(2) = 11436678 is the smallest solution of x = f^14(x).

Cf. A072137, A072141, A072142, A072143, A072718, A072719, A073142, A073144.

Offset changed by N. J. A. Sloane, Dec 01 2007

A073144 Smallest m such that the 'Reverse and Subtract' trajectory (cf. A072137) of m leads to A073142(n).

Original entry on oeis.org

0, 1012, 10001145, 100000114412, 100010505595

Offset: 1

Klaus Brockhaus, Jul 17 2002

Presumably a(6) = 1000000011011012.

			1012 -> 1089 -> 8712 -> 6534 -> 2178 = A073142(1) and no m < 1012 leads to 2178.

Cf. A072137, A072141, A072142, A072143, A072718, A072719, A073142, A073143.

Offset changed by N. J. A. Sloane, Dec 01 2007

A292992 Numbers n such that 13 applications of 'Reverse and Subtract' lead to n, whereas fewer than 13 applications do not lead to n.

Original entry on oeis.org

1195005230033599502088049947699664004979, 1381092199992389193086189078000076108069, 1417996648846699605185820033511533003948, 2845548027720844548271544519722791554517

Offset: 1

Ray Chandler, Sep 28 2017

There are 13 forty-digit terms in the sequence. Terms of derived sequences can be obtained either by inserting at the center of their digits any number of 9's or by concatenating a term any number of times with itself and inserting an equal number of 0's at all junctures.

			1195005230033599502088049947699664004979 -> 8598999439933899906714010005600661000932 -> 6208997779868899802537910022201311001974 -> 1417996648846699605185820033511533003948 -> 7075006702306600680629249932976933993193 -> 3161013305514201251368389866944857987486 -> 3686884278982488587263131157210175114127 -> 3527231431145022726364727685688549772736 -> 2845548027720844548271544519722791554517 -> 4309003944558309903456909960554416900965 -> 1381092199992389193086189078000076108069 -> 8226924500016320623717730754999836793762 -> 5552948110021750246544470518899782497534 ->
  1195005230033599502088049947699664004979.

Ray Chandler, Table of n, a(n) for n = 1..13
J. H. E. Cohn, Palindromic differences, Fibonacci Quart. 28 (1990), no. 2, 113-120.

Cf. A072142, A072143, A072718, A072719, A215669, A292634, A292635, A292846, A292856, A292857, A292858, A292859, A292993.

n = f^13(n), n <> f^k(n) for k < 13, where f: x -> |x - reverse(x)|.

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

Original entry on oeis.org

10695314508256806604321090888649339244708568530399, 11787342277647023379656208735392766826312885522179, 14638655404662283607788118901219361883250644206458, 26730889210860738952361172793674105293199801097128

Offset: 1

Ray Chandler, Sep 28 2017

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

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

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.

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

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

cp's OEIS Frontend

A292634 Numbers n such that 4 iterations of 'Reverse and Subtract' lead to n, whereas fewer than 4 iterations do not lead to n.

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A292635 Numbers n such that 5 applications of "Reverse and Subtract" lead to n, whereas fewer than 5 applications do not lead to n.

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A073142 List of smallest solutions for some k of x = f^k(x), n <> f^j(n) for j < k, where f: m -> |m - reverse(m)|.

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A073143 Numbers k such that A073142(n) = f^k(A073142(n)), where f: m -> |m - reverse(m)|.

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A073144 Smallest m such that the 'Reverse and Subtract' trajectory (cf. A072137) of m leads to A073142(n).

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A292992 Numbers n such that 13 applications of 'Reverse and Subtract' lead to n, whereas fewer than 13 applications do not lead to n.

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

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