A361199 a(1) = 1, a(2) = 2; for n >=3, a(n) is the number of primes in a(n-1), a(n-1) + a(n-2), ..., a(n-1) + a(n-2) + ... + a(1).

1, 2, 2, 2, 2, 1, 3, 2, 2, 3, 7, 2, 3, 7, 3, 5, 3, 7, 3, 7, 4, 4, 1, 10, 9, 2, 5, 7, 6, 4, 4, 5, 11, 8, 6, 2, 4, 7, 15, 6, 5, 10, 12, 9, 7, 11, 7, 14, 9, 8, 7, 16, 11, 9, 11, 10, 8, 7, 11, 13, 13, 9, 15, 9, 13, 14, 7, 15, 9, 12, 14, 15, 5, 13, 12, 6, 12, 9, 15

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(10) = 3 because three primes result from the adding up process, visualized below. These are 2, 7 and 17.
.                                                      Prime P/    Prime
a(1)  a(2)  a(3)  a(4)  a(5)  a(6)  a(7)  a(8)  a(9)  Composite C  Count
.
                                                  2  =   2  P        1
                                            2  +  2  =   4  C        0
                                      3  +  2  +  2  =   7  P        1
                                1  +  3  +  2  +  2  =   8  C        0
                          2  +  1  +  3  +  2  +  2  =  10  C        0
                    2  +  2  +  1  +  3  +  2  +  2  =  12  C        0
              2  +  2  +  2  +  1  +  3  +  2  +  2  =  14  C        0
        2  +  2  +  2  +  2  +  1  +  3  +  2  +  2  =  16  C        0
  1  +  2  +  2  +  2  +  2  +  1  +  3  +  2  +  2  =  17  P        1
                                                                 + _____
                                                         a(10)   =   3
.

Maple

A[1]:= 1: A[2]:= 2: S:= [0, 1, 3]:
for n from 3 to 100 do
  A[n]:= nops(select(isprime, map(t -> S[n]-t, S[1..n-1])));
  S:= [op(S), A[n]+S[-1]]
od:
seq(A[i], i=1..100); # Robert Israel, Mar 22 2023

Mathematica

a[1] = 1; a[2] = 2; a[n_] := a[n] = Count[Accumulate[Table[a[i], {i, n - 1, 1, -1}]], _?PrimeQ]; Array[a, 100] (* Amiram Eldar, Mar 04 2023 *)

Prog

(PARI) lista(nn) = my(va=vector(nn)); va[1] = 1; va[2] = 2; for (n=3, nn, my(s=0, nb=0); for (k=1, n-1, s += va[n-k]; if (isprime(s), nb++); ); va[n] = nb; ); va; \\ Michel Marcus, Mar 04 2023
(Python)
from sympy import isprime
from itertools import islice
def agen(): # generator of terms
    an, sums = 2, [1]
    yield 1
    while True:
        yield an
        sums = [s + an for s in sums] + [an]
        an = sum(1 for s in sums if isprime(s))
print(list(islice(agen(), 80))) # Michael S. Branicky, Mar 22 2023

Crossrefs

Cf. A000040, A361231, A361178.

Sequence in context: A306242 A118144 A136691 * A231168 A276830 A064741

Adjacent sequences: A361196 A361197 A361198 * A361200 A361201 A361202

Keyword

nonn

Author

Tamas Sandor Nagy, Mar 04 2023

Status

approved