A241658 Smallest semiprime, sp, such that n - sp is a semiprime, or a(n)=0 if there is no such sp.

0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 6, 4, 4, 6, 6, 0, 4, 4, 6, 6, 0, 9, 9, 4, 4, 6, 6, 4, 4, 6, 6, 0, 9, 9, 10, 4, 4, 4, 6, 6, 4, 4, 6, 6, 21, 9, 9, 10, 4, 25, 6, 4, 15, 4, 10, 6, 9, 4, 9, 4, 4, 6, 6, 10, 4, 9, 6, 4, 15, 6, 10, 4, 9, 6, 14, 15, 4, 10, 6, 4, 25, 6, 10, 34, 4, 10, 6, 4, 4

Offset

1,8

Comments

Conjecture: every number greater than 33 is a sum of two semiprimes. Only 1, 2, 3, 4, 5, 6, 7, 9, 11, 17, 22 & 33 cannot be so represented.

If n is prime, then a(2n) must be either 4 or an odd semiprime. See A241535.

First occurrence of the k-th semiprime (A001358): 8, 12, 23, 36, 76, 54, 46, 113, 51, 185, 254, 85, 294, 1881, 378, 1035, 1514, 634, 1509, 3550, 1621, 2713, 4050, 14788, 1485, 26839, 1497, 22694, 11965, 15334, 15810, 30894, 2721, 16849, ..., .

Links

Table of n, a(n) for n=1..90.

Example

a(23) = 9 because 23 = 9 + 14, two semiprimes.

Mathematica

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[{sp = 4}, While[ PrimeOmega[n - sp] != 2, sp = NextSemiPrime[sp]]; If[n > sp, sp, 0]]; Array[ f, 90]

Prog

(PARI) a(n) = {for (k=4, n-4, if ((bigomega(k) ==2) && (bigomega(n-k) == 2), return (k)); ); return (0); } \\ Michel Marcus, Jun 12 2014

Crossrefs

Cf. A001358, A241535, A241656.

Sequence in context: A292142 A345450 A098002 * A256719 A362209 A343722

Adjacent sequences: A241655 A241656 A241657 * A241659 A241660 A241661

Keyword

nonn

Author

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

Status

approved