cp's OEIS Frontend

A137779 Number of bases (numbering systems, including unary) in which the n-th prime is a palindrome having at least two digits.

%I A137779 #13 Jun 19 2014 22:50:10
%S A137779 1,2,3,3,2,3,4,2,3,3,4,3,3,3,2,2,3,3,4,3,4,2,3,3,3,3,2,4,4,3,4,3,2,2,
%T A137779 2,4,4,2,2,4,2,4,5,3,4,3,4,2,4,3,3,3,4,3,6,2,2,4,4,3,2,2,4,2,5,2,3,5,
%U A137779 2,3,5,2,2,6,5,3,2,3,4,4,4,5,3,4,2,5,3,4,4,4,3,3,4,2,3,3,3,4,4
%N A137779 Number of bases (numbering systems, including unary) in which the n-th prime is a palindrome having at least two digits.
%C A137779 Each prime p > 2 is palindrome in at least base 1 and base p-1, since p = 1*(p-1)^1 + 1*(p-1)^0 and p = 1*1^(p-1) + 1*1(p-2) + ... + 1*1^1 + 1*1^0.
%H A137779 Attila Olah, <a href="/A137779/b137779.txt">Table of n, a(n) for n = 1..10000</a>
%F A137779 a(n) = A126071(prime(n)). - _Charles R Greathouse IV_, Jun 19 2014
%e A137779 a(621) = 9 because the 621st prime (4591) is a palindrome in 9 bases: base 1, 19, 20, 24, 33, 37, 51, 54 and 4590 (4591 = 1*4590^1 + 1*4590^0).
%o A137779 (PARI) ispal(v) = {for(i=1, #v\2, if (v[i] != v[#v-i+1], return(0));); return(1);};
%o A137779 a(n) = {p = prime(n); 1 + sum(i=2, p, ispal(digits(p, i)));} \\ _Michel Marcus_, Sep 04 2013
%Y A137779 Cf. A087911, A126071.
%K A137779 easy,base,nonn
%O A137779 1,2
%A A137779 Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008