A090708 Primes whose decimal representation is a valid number in base 5 and interpreted as such is again a prime.

2, 3, 23, 43, 131, 241, 313, 401, 1123, 1231, 1321, 2111, 2113, 2221, 2311, 3323, 4003, 4241, 4423, 10103, 10301, 10433, 11243, 11423, 12011, 12413, 13331, 14323, 14411, 20113, 20201, 20443, 21011, 21143, 21341, 21433, 22111, 22133, 22441, 23431, 24113, 24421, 24443, 30211, 31223

Offset

1,1

Links

Alejandro J. Becerra Jr., Table of n, a(n) for n = 1..210

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

Example

23 is prime when read as base-10 number and also when read as base-5 number, 23 [base 5] = 13 [base 10].

Mathematica

Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 5], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *)

Prog

(PARI) fixBase(n, oldBase, newBase)=my(d=digits(n, oldBase), t=newBase-1); for(i=1, #d, if(d[i]>t, for(j=i, #d, d[j]=t); break)); fromdigits(d, newBase)
list(lim)=my(v=List(), t); forprime(p=2, fixBase(lim\1, 10, 5), if(isprime(t=fromdigits(digits(p, 5), 10)), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016
(Magma) [n:n in PrimesUpTo(32000)| Max(Intseq(n, 10)) le 4 and IsPrime(Seqint(Intseq(Seqint(Intseq(n), 5))))]; // Marius A. Burtea, Jun 30 2019

Crossrefs

Cf. A031974, A089971, A089981, A090707, A090709, A090710, A235394, A235395, A000040.

Sequence in context: A215282 A356498 A309586 * A359406 A199342 A262838

Adjacent sequences: A090705 A090706 A090707 * A090709 A090710 A090711

Keyword

base,nonn

Author

Cino Hilliard, Jan 18 2004

Extensions

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

More terms from Alejandro J. Becerra Jr., Aug 13 2018

Status

approved