A065725 Primes p such that the decimal expansion of its base-7 conversion is also prime.

2, 3, 5, 17, 29, 31, 43, 59, 71, 127, 157, 197, 211, 227, 239, 241, 337, 353, 367, 379, 409, 463, 491, 563, 577, 619, 647, 743, 757, 773, 787, 857, 911, 953, 967, 1093, 1123, 1163, 1193, 1249, 1303, 1373, 1429, 1459, 1471, 1499, 1583, 1597, 1613, 1627, 1669

Offset

1,1

Comments

In general rebase notation (Marc LeBrun): p7 = (7) [p] (10).

Links

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

Example

E.g., 787_10 = 2203_7 is prime, and so is 2203_10.

Mathematica

Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 7]]] & ]
Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 7]]]&] (* Harvey P. Dale, Nov 10 2022 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 7), 10)); \\ Michel Marcus, Mar 05 2022

Crossrefs

Primes in A036961.

Cf. A065720 up to A065727, A065361.

Sequence in context: A127061 A215311 A215315 * A057468 A127062 A214735

Adjacent sequences: A065722 A065723 A065724 * A065726 A065727 A065728

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 2001

Status

approved