OFFSET
1,3
COMMENTS
502743678 is the first value of n > 1 with a(n) = 0.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Mixed sums of primes and other terms, in: Additive Number Theory (edited by D. Chudnovsky and G. Chudnovsky), pp. 341-353, Springer, New York, 2010.
Zhi-Wei Sun, Conjectures on representations involving primes, in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II, Springer Proc. in Math. & Stat., Vol. 220, Springer, Cham, 2017, pp. 279-310. (See also arXiv:1211.1588 [math.NT], 2012-2017.)
EXAMPLE
a(2) = 1 since 2*2 = 2 + 3^0 + binomial(2*0,0) with 2 prime.
a(3) = 2 since 2*3 = 3 + 3^0 + binomial(2*1,1) = 2 + 3^1 + binomial(2*0,0) with 3 and 2 both prime.
MATHEMATICA
c[n_]:=c[n]=Binomial[2n, n];
tab={}; Do[r=0; k=0; Label[bb]; If[c[k]>=2n, Goto[aa]]; Do[If[PrimeQ[2n-c[k]-3^m], r=r+1], {m, 0, Log[3, 2n-c[k]]}]; k=k+1; Goto[bb]; Label[aa]; tab=Append[tab, r], {n, 1, 90}]; Print[tab]
CROSSREFS
Cf. A000040, A000224, A000984, A118955, A156695, A273812, A302982, A302984, A303233, A303234, A303338, A303363, A303389, A303393, A303399, A303428, A303401, A303432, A303434, A303539, A303540, A303541, A303543, A303601, A303637, A303639, A303656, A303660, A303702, A303821, A303932, A303934, A303998.
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 04 2018
STATUS
approved