A122381 Numbers n such that A014148[n] is a prime.

1, 2, 3, 6, 10, 23, 31, 46, 55, 58, 66, 70, 82, 91, 118, 131, 151, 163, 182, 187, 198, 199, 203, 222, 275, 279, 334, 346, 351, 358, 402, 411, 462, 470, 515, 582, 591, 619, 639, 650, 667, 671, 679, 706, 739, 750, 767, 835, 851, 875, 882, 899, 919, 926, 962, 966

Offset: 1

Author

Alexander Adamchuk, Aug 30 2006

Keywords

• nonn

Comments

Corresponding primes are listed in A122382[n] = A014148[ a(n) ] = {2,7,17,103,467,6577,17189,61627,109919,130531,198109,239579,399557,559313,...}.

Examples

			A014148[n] begins {2,7,17,34,62,103,161,238,338,467,627,824,1062,1343,...}.
a(1) = 1 because A014148[1] = 2 is prime.
a(2) = 2 because A014148[2] = 7 is prime.
		

Crossrefs

Cf. A014148, A122382.

Programs

Mathematica

p=0;s=0;f=0;Do[p=Prime[n];s=s+p;f=f+s;If[PrimeQ[f],Print[{n,f}]],{n,1,2000}]
Position[Nest[Accumulate,Prime[Range[1000]],2],?PrimeQ]//Flatten (* _Harvey P. Dale, Jul 15 2023 *)

Formula

A014148[n] = Sum[ Sum[ Prime[k], {k,1,m} ], {m,1,n} ]. A014148[ a(n) ] = A122382[n].