A180152 Numbers k such that the sum of the first k semiprimes is a prime.

3, 4, 5, 7, 8, 15, 21, 22, 37, 56, 59, 62, 82, 85, 89, 91, 114, 119, 121, 129, 139, 146, 168, 169, 189, 195, 197, 214, 227, 258, 286, 295, 312, 333, 341, 352, 360, 361, 387, 400, 419, 426, 434, 437, 440, 466, 470, 483, 495, 497, 504, 556, 595, 610, 619, 629, 636

Offset: 1

Author

Jason G. Wurtzel, Aug 13 2010

Keywords

• nonn

Examples

			21 is a term because the sum of the first 21 semiprimes is 647, which is prime.
		

Links

• K. Brockhaus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062198, A000040.

Programs

Magma

SP:=[ n: n in [2..3000] | &+[ k[2]: k in Factorization(n) ] eq 2 ]; V:=[]; s:=0; for j in [1..640] do s+:=SP[j]; if IsPrime(s) then Append(~V, j); end if; end for; V; // Klaus Brockhaus, Aug 14 2010

Maple

A062198 := proc(n) add( A001358(i),i=1..n) ; end proc:
isA180152 := proc(n) isprime( A062198(n)) ; end proc:
for n from 1 to 1000 do if isA180152(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Aug 14 2010

Mathematica

Position[Accumulate[Select[Range[10000],PrimeOmega[#]==2&]],?PrimeQ] // Flatten (* _Harvey P. Dale, Feb 17 2021 *)

Extensions

More terms from Klaus Brockhaus and R. J. Mathar, Aug 14 2010