

A241656


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


1



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
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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 kth 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: A059656 A205373 A064041 * 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



