A065047 Primes which when written in base 2 and prepended with a 1 produce a prime.

3, 5, 13, 29, 37, 43, 71, 83, 101, 113, 163, 193, 211, 223, 257, 311, 317, 347, 479, 509, 547, 577, 613, 643, 673, 709, 787, 823, 853, 877, 883, 907, 1031, 1061, 1181, 1223, 1259, 1283, 1409, 1451, 1481, 1493, 1499, 1511, 1523, 1559, 1583, 1721, 1871, 1973

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

13 is in the sequence because 13_10 = 1101_2 and prepending a 1 gives 11101_2 = 29_10, which is a prime.

Mathematica

Do[p = Prime[n]; d = IntegerDigits[p, 2]; If[ PrimeQ[ FromDigits[ Prepend[d, 1], 2]], Print[p]], {n, 1, 350} ]
Select[Prime[Range[300]], PrimeQ[FromDigits[Join[{1}, IntegerDigits[#, 2]], 2]]&] (* Harvey P. Dale, Apr 10 2023 *)

Prog

(PARI) { n=0; t=log(2); for (m=1, 10^9, p=prime(m); if (isprime(p + 2^(1 + log(p)\t)), write("b065047.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 05 2009

Crossrefs

Cf. A059459.

Sequence in context: A077443 A147196 A110225 * A282565 A295617 A290113

Adjacent sequences: A065044 A065045 A065046 * A065048 A065049 A065050

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Nov 05 2001

Status

approved