A341984 - OEIS

%I #5 Feb 24 2021 21:47:35

%S 1,5,15,30,50,71,100,130,170,195,231,250,310,340,420,430,525,535,685,

%T 680,851,800,1025,970,1280,1145,1470,1250,1685,1440,1991,1600,2230,

%U 1790,2615,2070,2985,2190,3250,2410,3700,2665,4125,2840,4560,3200,5135,3470,5670,3705,6226,4120

%N Number of ways to write n as an ordered sum of 5 primes (counting 1 as a prime).

%F G.f.: ( x + Sum_{k>=1} x^prime(k) )^5.

%p b:= proc(n) option remember; series(`if`(n=0, 1, x*add(

%p       `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 6)

%p     end:

%p a:= n-> coeff(b(n), x, 5):

%p seq(a(n), n=5..56);  # _Alois P. Heinz_, Feb 24 2021

%t nmax = 56; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &

%Y Cf. A008578, A280917, A283762, A340961, A341948, A341976, A341982, A341983.

%K nonn

%O 5,2

%A _Ilya Gutkovskiy_, Feb 24 2021