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.

2, 19, 83, 223, 277, 499, 1327, 1747, 2857, 11351, 10831, 11801, 12239, 12211, 18127, 21787, 36709, 30763, 16703

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

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).

Examples

			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.
		

Crossrefs

Cf. A007500.