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A115231
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Primes p which cannot be written in the form 2^i + q^j where i >= 0, j >= 1, q = odd prime.
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6
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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
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1,1
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COMMENTS
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Union with A115232 gives all primes (A000040).
All terms > 3 are in A095842. - M. F. Hasler, Nov 20 2014
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LINKS
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David A. Corneth, Table of n, a(n) for n = 1..11532 (terms <= 10^6)
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EXAMPLE
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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).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A095842, A115230, A115232, A115233, A000079, A061345.
Sequence in context: A254787 A042073 A124236 * A042369 A328257 A042701
Adjacent sequences: A115228 A115229 A115230 * A115232 A115233 A115234
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Jan 17 2006
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EXTENSIONS
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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
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STATUS
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approved
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