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A241535 Smallest semiprime q such that 2*prime(n) - q is semiprime, or a(n)=0 if there is no such q. 6
0, 0, 4, 4, 0, 4, 9, 4, 21, 9, 4, 9, 25, 4, 9, 15, 25, 4, 15, 9, 4, 15, 21, 9, 9, 15, 4, 9, 4, 9, 33, 9, 9, 4, 9, 4, 9, 21, 15, 25, 35, 4, 21, 4, 33, 4, 9, 9, 9, 4, 15, 9, 4, 9, 9, 9, 9, 4, 9, 9, 4, 21, 25, 25, 4, 51, 33, 25, 9, 4, 9, 15, 21, 9, 9, 21, 15, 9, 9, 15, 21, 4, 21, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: every even semiprime more than 22 is a sum of two semiprimes.

All terms are either 4 or odd.

First occurrence of k-th odd semiprime (A046315): 7, 16, 9, 13, 31, 41, 104, 134, 66, 412, 2769, 447, 1282, 3868, 7003, 3601, 48649, 11016, 5379, 41644, 34575, 83474, 120165, 135566, 21335, 394140, 14899, 876518, 434986, 173914, 691409, 1854580, 3741206, 714807, 1001321, 6427837, 4267513, 14809496, 7795998, 26617567, 2001937, 13958857, 9217135, 18815676, ..., . - Robert G. Wilson v, Apr 26 2014

If a(n) = 4, then 2*prime(n)-4=2*(prime(n)-2) is a semiprime, thus prime(n)-2 is a prime, so prime(n) belongs to A006512 (greater of twin primes). - Michel Marcus, Mar 26 2015

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

EXAMPLE

Let n=16, then 2*prime(16) = 2*53 = 106. We have 106-4=102, 106-6=100, 106-9=97, 106-10=96, 106-14=92, 106-15=91 and only the last number is semiprime. So a(16)=15.

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[{p2 = 2 Prime[n], sp = 4}, While[ PrimeOmega[p2 - sp] != 2, sp = NextSemiPrime[sp]]; If[ sp != p2, sp, 0]]; Array[f, 75] (* Robert G. Wilson v, Apr 25 2014 *)

CROSSREFS

Cf. A001358, A241531, A241533.

Sequence in context: A004018 A253185 A028658 * A169784 A236929 A028642

Adjacent sequences:  A241532 A241533 A241534 * A241536 A241537 A241538

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Apr 25 2014

EXTENSIONS

More terms from Robert G. Wilson v, Apr 25 2014

STATUS

approved

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Last modified November 20 02:52 EST 2018. Contains 317370 sequences. (Running on oeis4.)