A127018 -id:A127018 - cp's OEIS frontend

A127019 a(n) is the least semiprime s such that s - 2*n is also a semiprime.

6, 10, 10, 14, 14, 21, 35, 22, 22, 26, 26, 33, 35, 34, 34, 38, 38, 46, 77, 46, 46, 58, 55, 57, 65, 58, 58, 62, 62, 69, 77, 74, 87, 74, 74, 82, 95, 82, 82, 86, 86, 93, 95, 94, 94, 106, 115, 106, 119, 106, 106, 118, 115, 118, 119, 118, 118, 122, 122, 129, 143, 133, 141, 134

Offset: 1

Rick L. Shepherd, Jan 02 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A127018, A020484.

N:= 500: # for terms before the first term > N
P:= select(isprime, [2,seq(i,i=3..N/2,2)]):
SP:= select(`<=`,{seq(seq(P[i]*P[j],i=1..j),j=1..nops(P))},N):
R:= NULL:
for n from 1 do
  Q:= SP intersect (SP +~ (2*n));
  if Q = {} then break fi;
  R:= R, min(Q)
od:
R; # Robert Israel, Jan 30 2025

sp=Select[Range[1000],PrimeOmega[#]==2&];seq={};Do[s=0;Until[t=sp[[s]]-2n;PrimeOmega[t]==2&&t>0,s++];AppendTo[seq,sp[[s]]],{n,64}];seq (* James C. McMahon, Dec 30 2024 *)

A241656 Smallest semiprime, sp, such that 2n - sp is a semiprime, or a(n)=0 if there is no such sp.

Original entry on oeis.org

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

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

nonn

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, ..., .

			a(12) = 9 because 2*12 = 24 = 9 + 15, two semiprimes.

Cf. A001358, A127018, A241535, A241658.

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]

cp's OEIS Frontend

A127019 a(n) is the least semiprime s such that s - 2*n is also a semiprime.

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