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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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1
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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
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OFFSET
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0,3
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COMMENTS
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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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LINKS
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FORMULA
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{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
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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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PROG
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(PARI) a(n)=if(n<4, return(if(n>2, 1, n))); my(k=n\2, p=prime(k-1), q=nextprime(p+1)); if(n%2, (q-p)*a(n-2), q-p + a(n-2)) \\ Charles R Greathouse IV, Sep 09 2016
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CROSSREFS
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KEYWORD
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nonn,tabf,less
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AUTHOR
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STATUS
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approved
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