A115231 Primes p which cannot be written in the form 2^i + q^j where i >= 0, j >= 1, q = odd prime.

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

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: A042073 A124236 A371272 * A378839 A371231 A042369

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