A360757 Numbers k for which the arithmetic derivative of k is a Sophie Germain prime (A005384).

6, 42, 154, 182, 222, 231, 286, 357, 434, 442, 455, 483, 582, 595, 645, 690, 742, 762, 770, 806, 861, 906, 969, 987, 994, 1045, 1066, 1086, 1122, 1162, 1463, 1534, 1547, 1554, 1582, 1738, 1742, 1771, 1798, 1869, 1905, 2065, 2121, 2193, 2265, 2274, 2282, 2365

Offset: 1

Author

Marius A. Burtea, Mar 01 2023

Keywords

• nonn

Examples

			6' = 5 is prime and 2*6' + 1 = 2*5 + 1 = 11 is prime, so 6 is a term.
42' = 41 is prime and 2*42' + 1 = 2*41 + 1 = 83 is prime, so 42 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A005384.

Subsequence of A157037.

Programs

Magma

f:=func; [p:p in [1..2500]| IsPrime(Floor(f(p))) and IsPrime(2*Floor(f(p))+1) ];

Maple

filter:= proc(n) local np,t;
  np:= n*add(t[2]/t[1], t = ifactors(n)[2]);
  isprime(np) and isprime(2*np+1)
end proc:
select(filter, [$1..3000]); # Robert Israel, Mar 18 2023

Mathematica

d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[2400], PrimeQ[d1 = d[#]] && PrimeQ[2*d1 + 1] &] (* Amiram Eldar, Mar 01 2023 *)