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

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, 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, 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

Offset

1,2

Comments

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.

Links

Attila Olah, Table of n, a(n) for n = 1..10000

Formula

a(n) = A126071(prime(n)). - Charles R Greathouse IV, Jun 19 2014

Example

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).

Prog

(PARI) ispal(v) = {for(i=1, #v\2, if (v[i] != v[#v-i+1], return(0)); ); return(1); };
a(n) = {p = prime(n); 1 + sum(i=2, p, ispal(digits(p, i))); } \\ Michel Marcus, Sep 04 2013

Crossrefs

Cf. A087911, A126071.

Sequence in context: A296611 A308661 A286104 * A191246 A248222 A107918

Adjacent sequences: A137776 A137777 A137778 * A137780 A137781 A137782

Keyword

easy,base,nonn

Author

Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008

Status

approved