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

%I A243441 #30 Feb 21 2024 10:54:47
%S A243441 2,3,5,17,43,163,277,311,347,373,461,479,571,643,673,821,853,857,881,
%T A243441 977,983,1013,1093,1103,1117,1181,1223,1297,1427,1433,1439,1481,1523,
%U A243441 1607,1613,1621,1823,1861,1871,1873,2003,2083,2281,2333,2393,2417,2467,2549
%N A243441 Primes p such that p + A000120(p) is also a prime, where A000120 = sum of digits in base 2 = Hamming weight.
%H A243441 Anthony Sand, <a href="/A243441/b243441.txt">Table of n, a(n) for n = 1..1000</a>
%e A243441 2 + digitsum(2,base=2) = 2 + digitsum(10) = 2 + 1 = 3, which is prime.
%e A243441 3 + digitsum(11) = 3 + 2 = 5.
%e A243441 5 + digitsum(101) = 5 + 2 = 7.
%e A243441 17 + digitsum(10001) = 17 + 2 = 19.
%e A243441 43 + digitsum(101011) = 43 + 4 = 47.
%t A243441 Select[Prime@ Range@ 400, PrimeQ[# + Total@ IntegerDigits[#, 2]] &] (* _Michael De Vlieger_, Nov 06 2018 *)
%o A243441 (PARI) lista(lim) = forprime(p=2,lim, if (isprime(p+hammingweight(p)), print1(p, ", "))); \\ _Michel Marcus_, Jun 10 2014
%Y A243441 Cf. A000120, A092391 (n + A000120(n)), A048519 (analog for base 10).
%Y A243441 Cf. A243442 (analog for p - A000120(p)).
%K A243441 nonn,base
%O A243441 1,1
%A A243441 _Anthony Sand_, Jun 05 2014
%E A243441 Name edited by _M. F. Hasler_, Nov 07 2018