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%I #17 Sep 08 2022 08:46:06
%S 2,3,5,7,13,23,37,53,73,103,107,131,211,227,263,277,307,337,373,401,
%T 431,433,463,467,521,541,547,557,577,631,643,661,673,701,1013,1063,
%U 1151,1153,1201,1223,1327,1423,1451,1453,1531,1567,1613,1627,1663,1721,2011,2017
%N Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.
%H Charles R Greathouse IV, <a href="/A235394/b235394.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) = 13_10 = prime(5), 13_8 = 3 + 1*8 = 11_10 = prime(4).
%e a(8) = 53_10 = prime(16), 53_8 = 3 + 5*8 = 43_10 = prime(14). - _Marius A. Burtea_, Jun 30 2019
%t Select[FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 8], PrimeQ]
%o (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 list(lim)=my(v=List(),t); forprime(p=2,fixBase(lim\1,10,8), if(isprime(t=fromdigits(digits(p,8),10)), listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Nov 07 2016
%o (Magma) [n:n in PrimesUpTo(2100)| Max(Intseq(n,10)) le 7 and IsPrime(Seqint(Intseq(Seqint(Intseq(n),8))))]; // _Marius A. Burtea_, Jun 30 2019
%Y Cf. A031974, A089971, A089981, A090707, A090708, A090709, A090710, A235395, A000040.
%K base,easy,nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 09 2014
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