The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335495 Numbers k with a Goldbach partition (p,q) such that k | (p*q +- 1). 4
 5, 8, 10, 12, 24, 30, 36, 40, 42, 48, 50, 56, 58, 60, 66, 70, 72, 74, 84, 90, 96, 106, 112, 120, 130, 132, 144, 156, 168, 170, 180, 184, 198, 204, 210, 216, 220, 222, 224, 228, 232, 234, 240, 246, 252, 260, 264, 276, 280, 288, 294, 296, 300, 304, 312, 318, 330, 336, 340 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert G. Wilson v, Jul 22 2020: (Start) 5 is the only odd member. To qualify as a Goldbach partition, an odd number candidate must have as its two primes, p&q, p=2 and q=n-2. p*q=2n-4 and 2n-4 (mod n) == -4. This will only work with 5 since -4 (mod 5) is 1. Few terms are twice a prime: 10, 58, 74, 106, 562, 1546, 2474, 2554, 2578, 3394, 3418, 3754, 4282, 6242, 6602, 8578, 10306, ..., . Number of terms less than or equal to 10^n: 3, 21, 149, 1181, 9919, ..., . (End) LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Goldbach Partition Wikipedia, Goldbach's conjecture EXAMPLE 5 is in the sequence since it has a Goldbach partition, (3,2) such that 5 | (3*2 - 1) = 5. 8 is in the sequence since it has a Goldbach partition, (5,3) such that 8 | (5*3 + 1) = 16. 10 is in the sequence since it has a Goldbach partition, (7,3) such that 10 | (7*3 - 1) = 20. 12 is in the sequence since it has a Goldbach partition, (7,5) such that 12 | (7*5 + 1) = 36. MATHEMATICA Table[If[Sum[Sign[(1 - Ceiling[(i (n - i) + 1)/n] + Floor[(i (n - i) + 1)/n]) + (1 - Ceiling[(i (n - i) - 1)/n] + Floor[(i (n - i) - 1)/n])] (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}] > 0, n, {}], {n, 400}] // Flatten fQ = Compile[{{n, _Integer}}, Block[{p = 3, q}, While[q = n - p; m = Mod[p*q, n]; p < q && ! PrimeQ@q || m != 1 && m + 1 != n, p = NextPrime@p]; p < q]]; Join[{5}, Select[ 2Range@ 175, fQ]] (* Robert G. Wilson v, Jul 22 2020 *) CROSSREFS Sequence in context: A314381 A325180 A087280 * A280537 A022413 A078781 Adjacent sequences:  A335492 A335493 A335494 * A335496 A335497 A335498 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jun 11 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 25 14:45 EST 2020. Contains 338625 sequences. (Running on oeis4.)