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

Author

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

Keywords

• easy
• base
• nonn

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A087911, A126071.

Programs

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

Formula

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