A168154 Numbers n such that the sum of binary digits in prime(1), ..., prime(n) is prime.

2, 3, 5, 8, 9, 15, 18, 21, 28, 34, 35, 45, 51, 53, 68, 77, 84, 86, 87, 90, 92, 102, 113, 116, 119, 121, 130, 131, 137, 149, 164, 174, 178, 192, 205, 210, 220, 221, 238, 240, 241, 250, 255, 275, 315, 318, 324, 344, 345, 363, 369, 375, 381, 386, 396, 397, 398, 404

Offset: 1

Author

M. F. Hasler, Nov 20 2009

Keywords

• nonn
• base
• easy

Comments

Indices of primes in A095375.

Links

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

Crossrefs

Cf. A168153.

Programs

Mathematica

Module[{nn=500,prs},prs=Table[IntegerDigits[p,2],{p,Prime[Range[nn]]}];Select[Range[nn],PrimeQ[Total[Flatten[Take[prs,#]]]]&]] (* Harvey P. Dale, Aug 28 2021 *)

PARI

s=0; for(n=1,999, isprime(s+=norml2(binary(prime(n)))) & print1(n", "))
is_A168154(n)=isprime(A095375(n))

PARI

s=n=0;forprime(p=2,1e9,n++;if(isprime(s+=hammingweight(p)), print1(n", "))) \\ Charles R Greathouse IV, Mar 29 2013

Extensions

Terms corrected by Charles R Greathouse IV, Mar 29 2013