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 A093161 Even integers k such that there exists a prime p with p = min{q: q prime and (k - q) prime} and (k - p) < p^3. 4
 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 36, 38, 42, 48, 52, 54, 58, 60, 66, 68, 72, 78, 80, 84, 88, 90, 94, 96, 98, 102, 108, 114, 118, 120, 122, 124, 126, 128, 138, 146, 148, 150, 158, 164, 174, 180, 188, 190, 192, 206, 208, 210, 212, 218, 220, 222, 224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is conjectured that the sequence is finite with last term a(104820) = 5714500178 and it is proven that there are no more terms below 4*10^18. This is an extension of A307542. - Corinna Regina Böger, Apr 14 2019 LINKS Corinna Regina Böger, Table of n, a(n) for n = 1..10000 Corinna Regina Böger, a-file, Table of n, a(n) for n=1..104820 John F. Nash, Jr., Goldbach Programs EXAMPLE 63274 is in the sequence because 63274 = 293 + 62981 is the Goldbach partition with the smallest prime and 293^3 = 25153757 is > 62981. [clarified by Corinna Regina Böger, Apr 22 2019] MAPLE isS := proc(n) local p; for p from 2 while p^3 < (n-p) do if isprime(p) and isprime(n-p) then return false fi od; true end: isa := n -> irem(n, 2) = 0 and isS(n): select(isa, [\$4..224]); # Peter Luschny, Apr 26 2019 MATHEMATICA okQ[n_] := Module[{p}, For[p = 2, p <= n/2, p = NextPrime[p], If[p^3 + p < n && PrimeQ[n - p], Return[False]]]; True]; Select[Range[4, 250, 2], okQ] (* Jean-François Alcover, Jun 11 2019, from PARI *) PROG (PARI) noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^3+p2 && n%2 == 0 && noSpecialGoldbach(n) \\ Corinna Regina Böger, Apr 14 2019 CROSSREFS Cf. A025018. Sequence in context: A103517 A163300 A193175 * A307782 A325038 A360127 Adjacent sequences: A093158 A093159 A093160 * A093162 A093163 A093164 KEYWORD easy,nonn AUTHOR Jason Earls, May 10 2004 EXTENSIONS New name by Corinna Regina Böger, Apr 27 2019 STATUS approved

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Last modified September 24 00:14 EDT 2023. Contains 365554 sequences. (Running on oeis4.)