A255161 Prime numbers with more than one 1 < k < 10 for which the base-k representation is palindromic.

2, 3, 5, 7, 17, 31, 67, 73, 107, 109, 127, 173, 191, 227, 257, 373, 701, 1667, 2293, 4289, 5189, 6761, 7517, 7703, 9103, 12547, 14891, 15083, 16319, 19433, 28807, 31727, 47653, 65537, 69313, 83269, 85093, 86293, 262657, 295433, 444713, 663571, 1053953, 1063613

Offset: 1

Author

Pierandrea Formusa, Feb 15 2015

Keywords

• nonn
• base

Examples

			17 belongs to the sequence as for more than one one-digit base (2 and 4) its base representation is palindromic (in base 2 the representation is 10001, in base 4 the representation is 101).
13 does not belong to the sequence since only in one one-digit base (namely, base 3) is its base representation (111) palindromic.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..3793 (all terms < 10^14).

Crossrefs

Cf. A087155 (without restriction k<10).

Programs

PARI

ispal(n,b)=my(v=digits(n,b));for(i=1,#v\2,if(v[i]!=v[#v+1-i],return(0)));1
is(n)=sum(b=2,9,ispal(n,b))>1 && isprime(n) \\ Charles R Greathouse IV, Feb 21 2015