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A154279
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List of pairs: {a(n),b(n)}: a(n)=Prime[n]-Prime[n-1]+a(n-1); b(n)=(Prime[n]-Prime[n-1])*b(n-1).
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0
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0, 1, 2, 1, 3, 1, 5, 2, 7, 4, 11, 16, 13, 32, 17, 128, 19, 256, 23, 1024, 29, 6144, 31, 12288, 37, 73728, 41, 294912, 43, 589824, 47, 2359296, 53, 14155776, 59, 84934656, 61, 169869312, 67, 1019215872, 71, 4076863488, 73, 8153726976, 79, 48922361856, 83
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| There are primes associated with the product sequence:
Flatten[Table[If[PrimeQ[b[n] - 1], b[n] - 1, If[PrimeQ[b[n] + 1], b[ n] + 1, {}]], {n, 0, 30}]].
{2, 2, 2, 3, 3, 17, 31, 127, 257, 6143, 12289, 73727, 294911, 14155777,
169869311, 4076863487, 1174136684543}
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FORMULA
| {a(n),b(n)}:
a(n)=Prime[n]-Prime[n-1]+a(n-1);
b(n)=(Prime[n]-Prime[n-1])*b(n-1).
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MATHEMATICA
| Clear[a, b];
a[0] = 0; a[1] = 2; a[n_] := a[n] = Prime[n] - Prime[n - 1] + a[n - 1];
b[0] = 1; b[1] = 1; b[n_] := b[n] = (Prime[n] - Prime[n - 1])*b[n - 1];
Flatten[Table[{a[n], b[n]}, {n, 0, 30}]]
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CROSSREFS
| A081411
Sequence in context: A085053 A104725 A011129 * A065370 A147783 A102614
Adjacent sequences: A154276 A154277 A154278 * A154280 A154281 A154282
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KEYWORD
| nonn,uned,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 06 2009
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