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

%I A090708 #43 Sep 08 2022 08:45:12
%S A090708 2,3,23,43,131,241,313,401,1123,1231,1321,2111,2113,2221,2311,3323,
%T A090708 4003,4241,4423,10103,10301,10433,11243,11423,12011,12413,13331,14323,
%U A090708 14411,20113,20201,20443,21011,21143,21341,21433,22111,22133,22441,23431,24113,24421,24443,30211,31223
%N A090708 Primes whose decimal representation is a valid number in base 5 and interpreted as such is again a prime.
%H A090708 Alejandro J. Becerra Jr., <a href="/A090708/b090708.txt">Table of n, a(n) for n = 1..210</a>
%H A090708 Alejandro J. Becerra Jr., <a href="https://github.com/ajbecerr/OEIS/blob/main/A089971%2C%20A089981%2C%20A090707-A090710%2C%20A235394-A235395.ipynb">Python code for computing terms of A089971, A089981, A090707-A090710, A235394-A235395</a>.
%e A090708 23 is prime when read as base-10 number and also when read as base-5 number, 23 [base 5] = 13 [base 10].
%t A090708 Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 5], PrimeQ] (* _Robert G. Wilson v_, Jan 05 2014 *)
%o A090708 (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)
%o A090708 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
%o A090708 (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
%Y A090708 Cf. A031974, A089971, A089981, A090707, A090709, A090710, A235394, A235395, A000040.
%K A090708 base,nonn
%O A090708 1,1
%A A090708 _Cino Hilliard_, Jan 18 2004
%E A090708 Name, example and offset corrected by _M. F. Hasler_, Jan 03 2014
%E A090708 More terms from _Alejandro J. Becerra Jr._, Aug 13 2018