A342606 -id:A342606 - cp's OEIS frontend

A342604 a(n) = Sum_{j=1..n} A003718(j-1)*prime(j).

2, 5, 10, 17, 39, 52, 69, 126, 195, 224, 255, 403, 649, 821, 868, 921, 1216, 1826, 2496, 2851, 2924, 3003, 3501, 4836, 6776, 8291, 8909, 9016, 9125, 9916, 12583, 17168, 21963, 24882, 25925, 26076, 26233, 27537, 32213, 41901, 54431, 64567, 69915, 71459, 71656, 71855, 73754, 81782, 100850, 129704

Offset: 1

J. M. Bergot and Robert Israel, Mar 16 2021

nonn

			a(3) = A003718(0)*prime(1) + A003718(1)*prime(2) + A003718(2)*prime(3) = 1*2 + 1*3 + 1*5 = 10.

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

Cf. A003718, A342605, A342606.

p:= 1: R:= NULL:
for n from 0 to 14 do
  for k from 0 to n do
    p:= nextprime(p);
    R:= R, binomial(n,k)*p
od od:
ListTools:-PartialSums([R]):

A342605 Numbers k such that A342604(k) is prime.

Original entry on oeis.org

1, 2, 4, 14, 20, 26, 31, 39, 42, 57, 64, 69, 87, 92, 114, 127, 150, 152, 172, 213, 274, 301, 326, 379, 436, 460, 499, 523, 597, 708, 747, 817, 819, 912, 1382, 1452, 1595, 1600, 1603, 1632, 1647, 1670, 1768, 1833, 1834, 1873, 1890, 1986, 2137, 2696, 2702, 2859, 3080, 3154, 3167, 3173, 3386, 3933

Offset: 1

J. M. Bergot and Robert Israel, Mar 16 2021

nonn

			a(3) = 4 is a term because A342604(4) = 17 is prime.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A342604, A342606.

p:= 1: R:= NULL:
for n from 0 to 14 do
  for k from 0 to n do
    p:= nextprime(p);
    R:= R, binomial(n,k)*p
od od:
S:= ListTools:-PartialSums([R]):
select(t -> isprime(S[t]), [$1..nops(S)]);

A342604(a(n)) = A342606(n).

cp's OEIS Frontend

A342604 a(n) = Sum_{j=1..n} A003718(j-1)*prime(j).

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