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, 15953, 18290, 21480, 30294, 38516, 54874, 70132, 85419, 99583, 142053, 155243, 182169, 220996

Offset: 1

Author

Jaycob Coleman, Sep 08 2013

Keywords

• nonn

Comments

Conjectures: (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.

Examples

			a(5) = 3, since A002182(5) = 12 = 23-11 = 19-7 = 17-5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..84

Crossrefs

Cf. A002182, A117825, A202472.

Formula

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

Extensions

More terms from Amiram Eldar, Nov 03 2024