The On-Line Encyclopedia of Integer Sequences (OEIS)

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A341983

Number of ways to write n as an ordered sum of 4 primes (counting 1 as a prime).
(history; published version)

#8 by Alois P. Heinz at Thu Feb 25 15:28:35 EST 2021

STATUS

editing

approved

#7 by Alois P. Heinz at Thu Feb 25 15:28:33 EST 2021

LINKS

Alois P. Heinz, <a href="/A341983/b341983.txt">Table of n, a(n) for n = 4..10000</a>

STATUS

approved

editing

#6 by Alois P. Heinz at Wed Feb 24 21:48:48 EST 2021

STATUS

editing

approved

#5 by Alois P. Heinz at Wed Feb 24 21:48:44 EST 2021

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

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Wed Feb 24 20:06:20 EST 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Wed Feb 24 19:38:14 EST 2021

CROSSREFS

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

#2 by Ilya Gutkovskiy at Wed Feb 24 19:31:34 EST 2021

NAME

allocated for Ilya GutkovskiyNumber of ways to write n as an ordered sum of 4 primes (counting 1 as a prime).

DATA

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

FORMULA

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

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.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Feb 24 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Wed Feb 24 19:31:34 EST 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved