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%I #22 Aug 29 2015 12:25:53
%S 1,121,12321,1234321,123454321,12345654321,1234567654321,
%T 123456787654321,12345678987654321,12345678911987654321,
%U 123456789112211987654321,1234567891122332211987654321,12345678911223344332211987654321,123456789112233445544332211987654321
%N Concatenation of the palindromic numbers (A002113) in increasing order up to the n-th term and then in decreasing order.
%C By definition, all terms are palindromes. Inspired by A261493.
%C There are no primes in this sequence up to a(1100).
%C 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.
%C 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
%H M. F. Hasler, <a href="/A261570/b261570.txt">Table of n, a(n) for n = 1..108</a>
%e a(4) is the concatenation of 1, 2, 3 and 4, and then 3, 2 and 1 which results in 1234321.
%t 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]
%o (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 */
%o A261570(n,S=A002113(n))={while(n--,S=Str(A002113(n),S,A002113(n)));eval(S)} \\ _M. F. Hasler_, Aug 29 2015
%Y Cf. A002113, A173426, A261493, A261411.
%K nonn,easy,base
%O 1,2
%A _Robert G. Wilson v_, Aug 24 2015
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