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

1,1

Links

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

Example

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

Mathematica

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

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

Crossrefs

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

Sequence in context: A211073 A182315 A233862 * A126092 A132394 A295262

Adjacent sequences: A235391 A235392 A235393 * A235395 A235396 A235397

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Jan 09 2014

Status

approved