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
Examples
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.
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.
Programs
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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 *)
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PARI
forprime(p=2,1e4, if(isprime(t=fromdigits(digits(p,4))), print1(t", "))) \\ Charles R Greathouse IV, Apr 22 2015
Extensions
Name, example and offset corrected by M. F. Hasler, Jan 03 2014