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 A115231 Primes p which cannot be written in the form 2^i + q^j where i >= 0, j >= 1, q = odd prime. 6
 2, 3, 149, 331, 373, 509, 701, 757, 809, 877, 907, 997, 1019, 1087, 1259, 1549, 1597, 1619, 1657, 1759, 1777, 1783, 1867, 1973, 2293, 2377, 2503, 2579, 2683, 2789, 2843, 2879, 2909, 2999, 3119, 3163, 3181, 3187, 3299, 3343, 3433, 3539, 3643, 3697, 3739, 3779 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Union with A115232 gives all primes (A000040). All terms > 3 are in A095842. - M. F. Hasler, Nov 20 2014 LINKS David A. Corneth, Table of n, a(n) for n = 1..11532 (terms <= 10^6) EXAMPLE A000040(35) = 149 = 2^7+3*7 = 2^6+5*17 = 2^5+3*3*13 = 2^4+7*19 = 2^3+3*47 = 2^2+5*29 = 2^1+3*7*7 = 2^0+2*2*37, therefore 149 is a term (A115230(35)=0). MATHEMATICA maxp = 3779; Complement[pp = Prime[Range[PrimePi[maxp]]], Union[Sort[Reap[Do[p = 2^i + q^j; If[p <= maxp && PrimeQ[p], Sow[p]], {i, 0, Log[2, maxp]//Ceiling}, {j, 1, Log[3, maxp]//Ceiling}, {q, Rest[pp]} ]][[2, 1]]]]] (* Jean-François Alcover, Aug 03 2018 *) PROG (PARI) upto(n) = {my(pr = primes(primepi(n)), found = List(), s); for(i = 0, logint(n, 2), s = 2^i; forprime(q = 3, n - 2^i, for(j = 1, logint(n - 2^i, q), listput(found, s + q^j)))); listsort(found, 1); setminus(Set(pr), Set(found))} \\ David A. Corneth, Aug 03 2018 CROSSREFS Cf. A095842, A115230, A115232, A115233, A000079, A061345. Sequence in context: A254787 A042073 A124236 * A042369 A328257 A042701 Adjacent sequences:  A115228 A115229 A115230 * A115232 A115233 A115234 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jan 17 2006 EXTENSIONS Recomputed (based on recomputation of A115230) by R. J. Mathar and Reinhard Zumkeller, Apr 29 2010. Edited by N. J. A. Sloane, Apr 30 2010 2, 3 inserted by David A. Corneth, Aug 03 2018 STATUS approved

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Last modified January 16 17:26 EST 2021. Contains 340206 sequences. (Running on oeis4.)