A235394 Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.

2, 3, 5, 7, 13, 23, 37, 53, 73, 103, 107, 131, 211, 227, 263, 277, 307, 337, 373, 401, 431, 433, 463, 467, 521, 541, 547, 557, 577, 631, 643, 661, 673, 701, 1013, 1063, 1151, 1153, 1201, 1223, 1327, 1423, 1451, 1453, 1531, 1567, 1613, 1627, 1663, 1721, 2011, 2017

Offset: 1

Author

Robert G. Wilson v, Jan 09 2014

Keywords

• base
• easy
• nonn

Examples

			a(5) = 13_10 = prime(5), 13_8 = 3 + 1*8 = 11_10 = prime(4).
a(8) = 53_10 = prime(16), 53_8 = 3 + 5*8 = 43_10 = prime(14). - _Marius A. Burtea_, Jun 30 2019
		

Links

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

Crossrefs

Cf. A031974, A089971, A089981, A090707, A090708, A090709, A090710, A235395, A000040.

Programs

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

Mathematica

Select[FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 8], PrimeQ]

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\1,10,8), if(isprime(t=fromdigits(digits(p,8),10)), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016