A341983 Number of ways to write n as an ordered sum of 4 primes (counting 1 as a prime).

1, 4, 10, 16, 23, 28, 38, 44, 55, 52, 62, 60, 84, 80, 106, 88, 123, 108, 160, 128, 184, 136, 214, 168, 261, 172, 270, 168, 304, 204, 352, 200, 382, 232, 442, 264, 470, 232, 502, 268, 557, 300, 608, 292, 672, 340, 722, 372, 789, 356, 856, 396, 900, 432, 968, 380, 1024, 432

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..10000

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^4.

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 5)
    end:
a:= n-> coeff(b(n), x, 4):
seq(a(n), n=4..61);  # Alois P. Heinz, Feb 24 2021

Mathematica

nmax = 61; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &

Crossrefs

Cf. A008578, A280917, A283762, A340960, A341947, A341975, A341982, A341984.

Sequence in context: A294980 A310534 A357688 * A184527 A246297 A049881

Adjacent sequences: A341980 A341981 A341982 * A341984 A341985 A341986

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved