A243441 Primes p such that p + A000120(p) is also a prime, where A000120 = sum of digits in base 2 = Hamming weight.

2, 3, 5, 17, 43, 163, 277, 311, 347, 373, 461, 479, 571, 643, 673, 821, 853, 857, 881, 977, 983, 1013, 1093, 1103, 1117, 1181, 1223, 1297, 1427, 1433, 1439, 1481, 1523, 1607, 1613, 1621, 1823, 1861, 1871, 1873, 2003, 2083, 2281, 2333, 2393, 2417, 2467, 2549

Offset: 1

Author

Anthony Sand, Jun 05 2014

Keywords

• nonn
• base

Examples

			2 + digitsum(2,base=2) = 2 + digitsum(10) = 2 + 1 = 3, which is prime.
3 + digitsum(11) = 3 + 2 = 5.
5 + digitsum(101) = 5 + 2 = 7.
17 + digitsum(10001) = 17 + 2 = 19.
43 + digitsum(101011) = 43 + 4 = 47.
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000120, A092391 (n + A000120(n)), A048519 (analog for base 10).

Cf. A243442 (analog for p - A000120(p)).

Programs

Mathematica

Select[Prime@ Range@ 400, PrimeQ[# + Total@ IntegerDigits[#, 2]] &] (* Michael De Vlieger, Nov 06 2018 *)

PARI

lista(lim) = forprime(p=2,lim, if (isprime(p+hammingweight(p)), print1(p, ", "))); \\ Michel Marcus, Jun 10 2014

Extensions

Name edited by M. F. Hasler, Nov 07 2018