A228945 Number of ways to write highly composite numbers (A002182(n)) as the difference of two primes, both <= 2*A002182(n).

0, 0, 1, 1, 3, 6, 6, 7, 11, 19, 25, 28, 40, 61, 87, 109, 138, 184, 326, 437, 550, 721, 935, 1103, 1326, 1792, 1903, 2351, 3261, 4119, 5773, 7386, 8736, 10307, 14404

Offset

1,5

Comments

a(n)=A202472(A002182(n)/2) for n>1.

Conjecture: (a) This sequence is strictly increasing beginning with n=7. (b) If p is the smallest prime with p>A002182(n)+1, then p-A002182(n) is prime. This is a strengthening of a conjecture regarding A117825.

Links

Table of n, a(n) for n=1..35.

Example

a(5)=3, since 12=23-11=19-7=17-5.

Crossrefs

Cf. A202472, A117825.

Sequence in context: A130482 A239318 A177783 * A348467 A178746 A229986

Adjacent sequences: A228942 A228943 A228944 * A228946 A228947 A228948

Keyword

more,nonn

Author

Jaycob Coleman, Sep 08 2013

Status

approved