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A137779 Number of bases (numbering systems, including unary) in which the n-th prime is a palindrome having at least two digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 07:48 EDT 2020. Contains 337442 sequences. (Running on oeis4.)