

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
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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, afile, 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 < (np) do
if isprime(p) and isprime(np) 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] (* JeanFrançois Alcover, Jun 11 2019, from PARI *)


PROG

(PARI) noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^3+p<n && isprime(np), return(0))); 1
is(n) = n>2 && n%2 == 0 && noSpecialGoldbach(n) \\ Corinna Regina Böger, Apr 14 2019


CROSSREFS

Cf. A025018.
Sequence in context: A103517 A163300 A193175 * A307782 A325038 A111305
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



