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A235614 Number of ordered ways to write n = k + m with k a term of A235592 and m a positive triangular number. 7
0, 0, 1, 1, 2, 2, 2, 2, 3, 2, 2, 4, 1, 3, 3, 2, 3, 3, 3, 3, 5, 2, 3, 5, 3, 3, 3, 2, 4, 6, 2, 4, 3, 2, 4, 4, 4, 2, 6, 4, 4, 6, 2, 5, 2, 3, 7, 5, 4, 4, 6, 1, 2, 6, 5, 4, 5, 4, 5, 5, 1, 4, 7, 5, 5, 4, 2, 3, 5, 4, 4, 8, 4, 6, 4, 4, 4, 1, 2, 4, 7, 5, 3, 5, 3, 5, 3, 2, 6, 6, 4, 6, 8, 1, 4, 5, 5, 4, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Conjecture: a(n) > 0 for all n > 2.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(13) = 1 since 13 = 3 + 10 with 3*4 - prime(3) = 7 prime and 10 = 4*5/2 a positive triangular number.

a(52) = 1 since 52 = 37 + 15 with 37*38 - prime(37) = 1249 prime and 15 = 5*6/2 a positive triangular number.

a(61) = 1 since 61 = 6 + 55 with 6*7 - prime(6) = 29 prime and 55 = 10*11/2 a positive triangular number.

a(313) = 1 since 313 = 37 + 276 with 37*38 - prime(37) = 1249 prime and 276 = 23*24/2 a positive triangular number.

MATHEMATICA

PQ[n_]:=PrimeQ[n(n+1)-Prime[n]]

TQ[n_]:=IntegerQ[Sqrt[8n+1]]

a[n_]:=Sum[If[PQ[k]&&TQ[n-k], 1, 0], {k, 1, n-1}]

Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000040, A000217, A235592, A235613.

Sequence in context: A134868 A322861 A237259 * A127417 A198897 A201375

Adjacent sequences:  A235611 A235612 A235613 * A235615 A235616 A235617

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 13 2014

STATUS

approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)