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A235703 Number of ordered ways to write n = p + q with p a term of A234695 and q a term of A235592. 3
0, 0, 0, 1, 2, 2, 3, 3, 3, 3, 4, 2, 3, 2, 2, 4, 3, 3, 3, 3, 5, 5, 4, 3, 4, 4, 3, 5, 3, 1, 5, 5, 3, 5, 2, 4, 4, 3, 5, 4, 4, 4, 6, 5, 4, 6, 5, 3, 6, 6, 6, 5, 2, 3, 4, 3, 5, 5, 4, 5, 6, 4, 3, 6, 4, 3, 6, 4, 4, 5, 3, 5, 3, 5, 6, 6, 5, 3, 6, 4, 2, 4, 1, 4, 5, 4, 5, 7, 5, 4, 6, 9, 5, 6, 4, 2, 6, 6, 2, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Conjecture: a(n) > 0 for all n > 3, and a(n) = 1 only for n = 4, 30, 83.

LINKS

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

EXAMPLE

a(4) = 1 since 4 = 2 + 2 with 2, prime(2) - 2 + 1 = 2 and 2*3 - prime(2) = 3 all prime.

a(30) = 1 since 30 = 3 + 27 with 3, prime(3) - 3 + 1 = 3 and 27*28 - prime(27) = 756 - 103 = 653 all prime.

a(83) = 1 since 83 = 13 + 70 with 13, prime(13) - 13 + 1 = 29 and 70*71 - prime(70) = 4970 - 349 = 4621 all prime.

MATHEMATICA

p[n_]:=PrimeQ[Prime[n]-n+1]

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

a[n_]:=Sum[If[p[Prime[k]]&&q[n-Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}]

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

CROSSREFS

Cf. A000040, A234695, A235330, A235508, A235592.

Sequence in context: A087182 A035453 A272605 * A097747 A285717 A115777

Adjacent sequences:  A235700 A235701 A235702 * A235704 A235705 A235706

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 14 2014

STATUS

approved

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)