

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
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OFFSET

1,5


COMMENTS

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


LINKS

ZhiWei 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[nPrime[k]], 1, 0], {k, 1, PrimePi[n1]}]
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

ZhiWei Sun, Jan 14 2014


STATUS

approved



