A241658 -id:A241658 - cp's OEIS frontend

A241656 Smallest semiprime, sp, such that 2n - sp is a semiprime, or a(n)=0 if there is no such sp.

0, 0, 0, 4, 4, 6, 4, 6, 4, 6, 0, 9, 4, 6, 4, 6, 9, 10, 4, 6, 4, 6, 21, 9, 4, 6, 15, 10, 9, 9, 4, 6, 4, 6, 15, 10, 9, 14, 4, 6, 25, 10, 4, 6, 4, 6, 9, 9, 4, 6, 9, 9, 15, 14, 4, 6, 21, 10, 25, 9, 4, 6, 4, 6, 9, 9, 15, 14, 4, 6, 9, 10, 4, 6, 4, 6, 9, 10, 15, 14, 4, 6, 21, 9, 4, 6, 15, 10, 9, 14

Offset: 1

Vladimir Shevelev and Robert G. Wilson v, Apr 26 2014

nonn

Conjecture: every even number greater than 22 is a sum of two semiprimes. Only 2, 4, 6 & 22 cannot be so represented.
If n is prime, then a(n) must be either 4 or an odd semiprime. See A241535.
First occurrence of the k-th semiprime (A001358): 4, 6, 12, 18, 38, 27, 23, 124, 41, 326, 127, 1344, 147, 1278, 189, 3294, 757, 317, 1362, 1775, 3300, 2504, 2025, 7394, 84848, 13899, 56584, 11347, 156396, 7667, 7905, 15447, 404898, 20937, ..., .

			a(12) = 9 because 2*12 = 24 = 9 + 15, two semiprimes.

Cf. A001358, A127018, A241535, A241658.

NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[ sgn < 0, sp--, sp++]]; If[ sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; f[n_] := Block[{en = 2 n, sp = 4}, While[ PrimeOmega[en - sp] != 2, sp = NextSemiPrime[sp]]; If[en > sp, sp, 0]]; Array[ f, 90]

cp's OEIS Frontend

A241656 Smallest semiprime, sp, such that 2n - sp is a semiprime, or a(n)=0 if there is no such sp.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica