A261570 Concatenation of the palindromic numbers (A002113) in increasing order up to the n-th term and then in decreasing order.

1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 12345678911987654321, 123456789112211987654321, 1234567891122332211987654321, 12345678911223344332211987654321, 123456789112233445544332211987654321

Offset

1,2

Comments

By definition, all terms are palindromes. Inspired by A261493.

There are no primes in this sequence up to a(1100).

The least prime factors of a(n), n>=1, are: 1, 11, 3, 11, 41, 3, 239, 11, 3, 11, 11, 3, 11, 11, 3, 11, 11, 3, 71, 21557, 19, 17, 31, 181, 17, 353, 19, 31, 19, 29, 17, 29, 11616377, 214141, 19, 5471, 17, 13883, 3, 7, ..., . See A261411.

The first (probable) prime in this sequence was found by David Broadhurst on Aug 25 2015: this is a(2007), a 21233-digit probable prime with central term 1008001. - N. J. A. Sloane, Aug 24 2015

Links

M. F. Hasler, Table of n, a(n) for n = 1..108

Example

a(4) is the concatenation of 1, 2, 3 and 4, and then 3, 2 and 1 which results in 1234321.

Mathematica

palQ[n_] := Reverse[idn = IntegerDigits@ n] == idn; s = Select[ Range @111, palQ]; f[n_] := FromDigits@ Flatten[ IntegerDigits@# & /@ Join[Take[s, n], Reverse@ Take[s, n - 1]]]; a = Array[f, 14]

Prog

(PARI) A002113(n)=if(n>9, (n-=9)*10+if(n>9, n\10, n), n)/* This "poor man's" version is valid only for n<109 */
A261570(n, S=A002113(n))={while(n--, S=Str(A002113(n), S, A002113(n))); eval(S)} \\ M. F. Hasler, Aug 29 2015

Crossrefs

Cf. A002113, A173426, A261493, A261411.

Sequence in context: A321687 A002477 A173426 * A068117 A080162 A030174

Adjacent sequences: A261567 A261568 A261569 * A261571 A261572 A261573

Keyword

nonn,easy,base

Author

Robert G. Wilson v, Aug 24 2015

Status

approved