A065723 - OEIS

A065723

Primes that when written in base 5, then reinterpreted in base 10, again give primes.

2, 3, 13, 23, 41, 71, 83, 101, 163, 191, 211, 281, 283, 311, 331, 463, 503, 571, 613, 653, 701, 743, 823, 863, 881, 983, 1091, 1213, 1231, 1283, 1301, 1373, 1381, 1423, 1471, 1493, 1531, 1543, 1621, 1741, 1783, 1861, 1873, 1931, 2063, 2203, 2213, 2221

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

In general rebase notation (Marc LeBrun): p5 = (5) [p] (10).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

E.g., 2213_10 = 32323_5 is prime, and so is 32323_10.

MATHEMATICA

Select[ Range[2250], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 5]]] & ]

Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 5]]]&] (* Harvey P. Dale, Mar 28 2015 *)