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A025127 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A000040 (primes). 1
3, 5, 7, 11, 13, 17, 30, 36, 46, 50, 60, 70, 74, 84, 94, 102, 108, 120, 161, 171, 187, 197, 209, 229, 243, 253, 271, 281, 289, 313, 323, 339, 363, 381, 391, 403, 421, 431, 530, 552, 568, 592, 618, 630, 650, 674, 696, 712, 746, 768, 794, 802, 830, 846, 872, 906, 922, 942, 962 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

MATHEMATICA

b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2, 3]], {m, 0, 15}];

A025127[n_]:= A025127[n]= Sum[b[n-j+2]*Prime[j], {j, Floor[(n+4)/2], n+1}];

Table[A025127[n], {n, 100}] (* G. C. Greubel, Sep 14 2022 *)

PROG

(Magma)

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

A025127:= func< n | (&+[NthPrime(n+2-k)*A023533(k): k in [1..Floor((n+1)/2)]]) >;

[A025127(n): n in [1..100]]; // G. C. Greubel, Sep 14 2022

(SageMath)

def b(j): return sum(bool(j==binomial(m+2, 3)) for m in (0..13))

@CachedFunction

def A025127(n): return sum(b(n-j+2)*nth_prime(j) for j in (((n+4)//2)..n+1))

[A025127(n) for n in (1..100)] # G. C. Greubel, Sep 14 2022

CROSSREFS

Cf. A000040, A023533.

Sequence in context: A239391 A087382 A355845 * A024883 A024328 A032529

Adjacent sequences: A025124 A025125 A025126 * A025128 A025129 A025130

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 3 01:46 EST 2023. Contains 360024 sequences. (Running on oeis4.)