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A124151
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Smallest k such that 1 + Sum{j=1..n} k^(2*j-1) is prime.
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3
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1, 1, 2, 1, 2, 1, 10, 2, 2, 1, 2, 1, 48, 182, 2, 1, 60, 1, 10, 42, 2, 1, 102, 12, 4, 12, 110, 1, 12, 1, 100, 5, 28, 18, 144, 1, 102, 9, 2, 1, 30, 1, 186, 110, 130, 1, 566, 23, 1234, 2, 12, 1, 336, 103, 142, 341, 1104, 1, 444, 1, 22, 119, 2, 45, 14, 1, 84, 23, 238, 1, 936, 1, 78, 12
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OFFSET
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1,3
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COMMENTS
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a(n) = 1 if and only if n is in A006093 (primes minus 1), so 1 occurs infinitely often.
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LINKS
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EXAMPLE
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Consider n = 7. 1 + Sum{j=1...7} k^(2*j-1) evaluates to 8, 10923, 1793614, 71582789, 1271565756, 13433856703, 98907531458, 558482096649, 2573639151184, 10101010101011 for k = 1, ..., 10. Only the last of these numbers, 1+10+10^3+10^5+10^7+10^9+10^11+10^13 = 10101010101011, is prime, hence a(7) = 10.
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[ !PrimeQ[Sum[k^(2j - 1), {j, n}] + 1], k++ ]; k]; Array[f, 74] (* Robert G. Wilson v, Dec 17 2006 *)
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PROG
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(PARI) {m=74; for(n=1, m, k=1; while(!isprime(1+sum(j=1, n, k^(2*j-1))), k++); print1(k, ", "))} - Klaus Brockhaus, Dec 16 2006
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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