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A077608
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Number of compositions of n into twin primes (i.e., primes that are members of a twin prime pair, like 3, 5, 7, 11, 13, but not 2 or 23).
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8
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1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 4, 3, 7, 7, 8, 14, 15, 21, 28, 33, 47, 58, 75, 103, 125, 167, 220, 275, 370, 474, 610, 806, 1028, 1347, 1752, 2253, 2954, 3812, 4944, 6451, 8329, 10841, 14077, 18226, 23720, 30745, 39903, 51857, 67214, 87313, 113340, 147017, 190974
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OFFSET
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0,9
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LINKS
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Iain Fox, Table of n, a(n) for n = 0..8834 (first 1001 terms from Alois P. Heinz)
P. Flajolet, Publications
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FORMULA
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G.f.: 1/(1 - Sum_{k>=1} x^A001097(k)). - Andrew Howroyd, Dec 28 2017
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EXAMPLE
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a(15) = 8 since 15 = 11+7 = 7+11 = 5+13 = 13+5 = 3+5+7 = 3+7+5 = 5+3+7 = 5+7+3 = 7+3+5 = 7+5+3 and 3,5,7,11 belong to twin pairs.
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MAPLE
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A077608 := proc(n) coeff(series(1/(1-add(z^numtheory[ithprime](j)* subs([true=1, false=0], evalb(isprime(ithprime(j)-2) or isprime(ithprime(j)+2))), j=2..n+2)), z=0, n+1), z, n): end;
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MATHEMATICA
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a[n_] := Coefficient[Series[ 1/(1 - Sum[z^Prime[j]*Boole[ PrimeQ[Prime[j] - 2] || PrimeQ[ Prime[j] + 2]], {j, 2, n + 2}]), {z, 0, n + 1}], z, n]; Table[a[n], {n, 0, 53}] (* Jean-François Alcover, Nov 09 2012, after Maple *)
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PROG
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(PARI)
ok(n)={isprime(n) && (isprime(n-2) || isprime(n+2))}
{my(n=60); Vec(1/(1-sum(k=1, n, if(ok(k), x^k, 0))) + O(x*x^n))} \\ Andrew Howroyd, Dec 28 2017
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CROSSREFS
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Cf. A001097, A002124, A023360.
Sequence in context: A022466 A144254 A133310 * A002124 A097564 A345233
Adjacent sequences: A077605 A077606 A077607 * A077609 A077610 A077611
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KEYWORD
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nonn
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AUTHOR
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Philippe Flajolet, Nov 11 2002
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STATUS
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approved
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