A265112 a(n) = A023360(A000040(n)): number of compositions of prime(n) into prime parts.

1, 1, 3, 6, 20, 46, 232, 501, 2352, 24442, 53243, 550863, 2616338, 5701553, 27077005, 280237217, 2900328380, 6320545915, 65414893802, 310664269401, 677015556295, 7006815193063, 33276323565116, 344395408399372, 7767597342090622, 36889382062795742

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..768

Example

prime(4) = 7; a(4) = A023360(7) = 6 because there are 6 compositions of 7 into prime parts {2,3,5,7}: {7}, {5+2}, {3+2+2}, {2+5}, {2+3+2} and {2+2+3}.

Maple

N:= 1000: # to get a(1) to a(A000720(N))
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
M:= nops(Primes);
F:= proc(x)
option remember;
local k;
add(procname(x-Primes[k]), k=1..numtheory:-pi(x));
end proc:
F(0):= 1:
seq(F(Primes[n]), n=1..M); # Robert Israel, Dec 02 2015

Mathematica

Needs["Combinatorica`"]; Table[Length@ Flatten[Permutations[#, {Length@ #}] & /@ Select[Combinatorica`Partitions@ Prime@ n, AllTrue[#, PrimeQ] &], 1], {n, 14}] (* Version 10, slow, or *)
lim = 101; t = Rest@ CoefficientList[Series[1/(1 - Sum[x^Prime[i], {i, 1, PrimePi@ lim}]), {x, 0, lim}], x]; t[[#]] &@ Prime@ Range@ PrimePi@ lim
(* Michael De Vlieger, Dec 01 2015, after David W. Wilson at A023360 *)

Crossrefs

Cf. A000040 (prime numbers), A023360.

Sequence in context: A339639 A081181 A062164 * A052408 A148573 A148574

Adjacent sequences: A265109 A265110 A265111 * A265113 A265114 A265115

Keyword

nonn,easy

Author

Bob Selcoe, Dec 01 2015

Status

approved