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A303660
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Number of ways to write 2*n+1 as p + 3^k + 5^m, where p is a prime, and k and m are nonnegative integers.
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13
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0, 1, 2, 3, 3, 4, 4, 4, 4, 5, 3, 4, 4, 3, 6, 7, 5, 6, 8, 5, 5, 9, 6, 5, 8, 3, 6, 8, 4, 4, 7, 6, 4, 8, 6, 5, 9, 4, 4, 8, 3, 6, 8, 7, 4, 9, 6, 4, 9, 5, 5, 9, 6, 6, 11, 7, 7, 9, 5, 3, 8, 5, 3, 9, 7, 7, 11, 8, 8, 12
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OFFSET
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1,3
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COMMENTS
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Note that a(21323543) = 0, i.e., the odd number 2*21323543 + 1 = 42647087 cannot be written as the sum of a prime, a power of 3 and a power of 5.
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LINKS
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EXAMPLE
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a(2) = 1 since 2*2+1 = 3 + 3^0 + 5^0 with 3 prime.
a(3) = 2 since 2*3+1 = 3 + 3^1 + 5^0 = 5 + 3^0 + 5^0 with 3 and 5 prime.
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MATHEMATICA
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tab={}; Do[r=0; Do[If[PrimeQ[2n+1-5^x-3^y], r=r+1], {x, 0, Log[5, 2n]}, {y, 0, Log[3, 2n+1-5^x]}]; tab=Append[tab, r], {n, 1, 70}]; Print[tab]
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CROSSREFS
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Cf. A000040, A000244, A000351, A273812, A302982, A302984, A303233, A303234, A303338, A303363, A303389, A303393, A303399, A303428, A303401, A303432, A303434, A303539, A303540, A303541, A303543, A303601, A303637, A303639, A303656.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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