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A107926
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The least number k such that there are primes p and q with p - q = 2*n, p + q = k, and p the least such prime >= k/2.
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6
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4, 8, 18, 16, 54, 48, 50, 108, 102, 44, 234, 444, 98, 228, 174, 92, 414, 432, 242, 516, 582, 256, 1182, 672, 406, 612, 846, 272, 1038, 984, 442, 1776, 1902, 292, 1074, 636, 1054, 3312, 1122, 476, 1398, 1464, 530, 1728, 2730, 572, 2706, 3348, 682, 2844, 3342
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OFFSET
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0,1
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COMMENTS
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From the Goldbach conjecture.
a(3n)> a(3n-2), a(3n-1), a(3n+1) & a(3n+2) for all n > 0 except for n = 1, 2, 12, 19, 20 or 41.
Except for 1, all indices, i, not congruent to 0 (mod 3), a(i) is congruent to 0 (mod 6) and for all indices, i, congruent to 0 (mod 3), a(i) is not congruent to 0 (mod 6). Of those not congruent to 0 (mod 6), those congruent to 2 outnumber those congruent to 4, about 8 to 7. Robert G. Wilson v, Nov 03 2013
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LINKS
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EXAMPLE
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a(0) = 4 because 4=2+2 and 2-2=0.
a(1) = 8 because 8 is the least number with 8=p+q and p-q=2 for primes p and q.
a(2) = 18 because 18=7+11 and the primes 7 and 11 have difference 4.
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MATHEMATICA
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f[n_] := For[p = n/2, True, p--, If[PrimeQ[p] && PrimeQ[n - p], Return[n/2 - p]]]; nn=101; t=Table[0, {nn}]; cnt=0; n=1; While[cnt<nn, n++; d=f[2n]; If[d+1<=nn && t[[d+1]]==0, t[[d+1]]=n; cnt++]]; 2t
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Gilmar J. Rodriguez (Gilmar.Rodriguez(AT)nwfwmd.state.fl.us) and Robert G. Wilson v, Jun 16 2005
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STATUS
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approved
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