A090707 Primes whose decimal representation is a valid number in base 4 and interpreted as such is again a prime.

2, 3, 11, 13, 23, 31, 101, 103, 113, 131, 211, 223, 233, 311, 331, 1013, 1021, 1033, 1103, 1201, 1213, 1223, 1231, 1301, 2003, 2111, 2113, 2131, 2203, 2213, 2311, 2333, 3001, 3011, 3203, 3221, 3301, 3323, 10111, 10211, 10303, 10313, 10321, 10331

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Alejandro J. Becerra Jr., Python code for computing terms of A089971, A089981, A090707-A090710, A235394-A235395.

Example

13 is prime in decimal and also when considered as a number in base 4: 13 [base 4] = 7 [base 10] which is also prime.

Mathematica

Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 4], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *)
FromDigits[#, 10]&/@Select[Tuples[{0, 1, 2, 3}, 5], AllTrue[{FromDigits[#, 4], FromDigits[#, 10]}, PrimeQ]&] (* Harvey P. Dale, Jul 30 2021 *)

Prog

(PARI) forprime(p=2, 1e4, if(isprime(t=fromdigits(digits(p, 4))), print1(t", "))) \\ Charles R Greathouse IV, Apr 22 2015

Crossrefs

Cf. A031974, A089971, A089981, A090708, A090709, A090710, A235394, A235395, A000040.

Sequence in context: A076503 A004678 A107715 * A062350 A163498 A038874

Adjacent sequences: A090704 A090705 A090706 * A090708 A090709 A090710

Keyword

base,nonn

Author

Cino Hilliard, Jan 18 2004

Extensions

Name, example and offset corrected by M. F. Hasler, Jan 03 2014

Status

approved