A065726 Primes p whose base-8 expansion is also the decimal expansion of a prime.

2, 3, 5, 7, 11, 19, 31, 43, 59, 67, 71, 89, 137, 151, 179, 191, 199, 223, 251, 257, 281, 283, 307, 311, 337, 353, 359, 367, 383, 409, 419, 433, 443, 449, 523, 563, 617, 619, 641, 659, 727, 787, 809, 811, 857, 887, 907, 919, 947, 977, 1033, 1039, 1097, 1123

Offset

1,1

Comments

In general rebase notation (Marc LeBrun): p8 = (8) [p] (10).

Links

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

M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Example

E.g., 787_10 = 1423_8 is prime, and so is 1423_10.

Mathematica

Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 8]]] & ]

Prog

(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 8); if (isprime(b), write("b065726.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 28 2009
(PARI) is(p, b=10, c=8)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ This code can be used for other bases b, c when b>c. See A235265 for code also valid for b<c. \\ M. F. Hasler, Jan 12 2014

Crossrefs

Cf. A065720 up to A065727, A065361.

Cf. A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A003064 A057429 A137814 * A215161 A227907 A118985

Adjacent sequences: A065723 A065724 A065725 * A065727 A065728 A065729

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 2001

Extensions

Definition clarified by M. F. Hasler, Jan 12 2014

Status

approved