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

Author

Robert G. Wilson v, Aug 24 2015

Keywords

• nonn
• easy
• base

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

Examples

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

Links

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

Crossrefs

Cf. A002113, A173426, A261493, A261411.

Programs

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]

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