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A135436 a(n) is the least prime for which the n-th term of the sequence S(a(n)) belongs to A007500, where each term of S(p) is the least prime >= the reversal of the previous term. 0
2, 19, 83, 223, 277, 499, 1327, 1747, 2857, 11351, 10831, 11801, 12239, 12211, 18127, 21787, 36709, 30763, 16703 (list; graph; refs; listen; history; text; internal format)



After a term of A007500 has appeared in S(p), either this number, if it's truly palindromic, or the pair constituted by it and its reversal, is repeated indefinitely.

For all primes <= 189989, a term of A007500 appears always in S(p) but I could not go further as in the sequence S(p) of the next prime appears a term > 10^6 which is beyond my capacities of calculation. Anyway it's not a surprise and very probably all sequences S(p) reach a stability in a finite limit. What is more surprising is that on the one hand the same term of A007500 appears in sequence S(n) for a(13) and a(14) and on the other hand another same term of A007500 appears in these sequences for a(16), a(17), a(18) and a(19).


Table of n, a(n) for n=1..19.


The sequence S(223) is 223, 331, 137, 733 = A007500(38) and that is wrong for any prime lower than 223. Hence a(4)= 223.


Cf. A007500.

Sequence in context: A327820 A331898 A054570 * A056005 A034572 A041393

Adjacent sequences: A135433 A135434 A135435 * A135437 A135438 A135439




Philippe LALLOUET (philip.lallouet(AT)orange.fr), Feb 18 2008



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Last modified December 3 13:06 EST 2022. Contains 358524 sequences. (Running on oeis4.)