

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
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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]]]]] (* JeanFrançois 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



