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

1,2

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,...}.

Links

Table of n, a(n) for n=1..56.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A014148, A122382.

Sequence in context: A002992 A130867 A218210 * A141034 A300442 A152536

Adjacent sequences: A122378 A122379 A122380 * A122382 A122383 A122384

Keyword

nonn

Author

Alexander Adamchuk, Aug 30 2006

Status

approved