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A241658 Smallest semiprime, sp, such that n - sp is a semiprime, or a(n)=0 if there is no such sp. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A035638 A292142 A098002 * A256719 A035622 A112919

Adjacent sequences:  A241655 A241656 A241657 * A241659 A241660 A241661

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 23 15:00 EST 2020. Contains 332166 sequences. (Running on oeis4.)