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Search: id:A124151
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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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5
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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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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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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 (rgwv(at)rgwv.com), Dec 17 2006 *)
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PROGRAM
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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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Cf. A006093, A124205-A124209, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124154, A124163.
Sequence in context: A104060 A062347 A124781 this_sequence A110179 A071559 A071560
Adjacent sequences: A124148 A124149 A124150 this_sequence A124152 A124153 A124154
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006, Dec 14 2006
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 16 2006
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