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A219533
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a(n) = smallest prime not included earlier such that a(n-4) + a(n-3) + a(n-2) + a(n-1) + a(n) is a prime, with a(1)=3, a(2)=5, a(3)=7, and a(4)=11.
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1
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3, 5, 7, 11, 17, 13, 19, 23, 29, 43, 37, 31, 41, 47, 67, 53, 61, 79, 71, 73, 83, 103, 59, 101, 97, 89, 157, 113, 107, 127, 109, 131, 139, 137, 167, 199, 179, 181, 151, 149, 163, 233, 191, 193, 173, 223, 197, 211, 227, 229, 239, 257, 241, 251, 271, 263, 277, 311, 307, 269
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(5) = 17 because 13 will not work (3 + 5 + 7 + 11 + 13 = 39) but 17 does work, with 3 + 5 + 7 + 11 + 17 = 43.
a(6) = 13 because it is the smallest prime that will produce the desired result: 5 + 7 + 11 + 17 + 13 = 53.
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MATHEMATICA
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f[s_List] := Block[{p = s[[-4]] + s[[-3]] + s[[-2]] + s[[-1]], q = 13}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q]]; Append[s, q]]; Nest[f, {3, 5, 7, 11}, 56]
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CROSSREFS
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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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