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

1,4

Comments

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, ..., .

Links

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

Example

a(12) = 9 because 2*12 = 24 = 9 + 15, 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[{en = 2 n, sp = 4}, While[ PrimeOmega[en - sp] != 2, sp = NextSemiPrime[sp]]; If[en > sp, sp, 0]]; Array[ f, 90]

Crossrefs

Cf. A001358, A241535, A241658.

Sequence in context: A205373 A064041 A365476 * A275161 A077553 A010659

Adjacent sequences: A241653 A241654 A241655 * A241657 A241658 A241659

Keyword

nonn

Author

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

Status

approved