OFFSET
0,1
COMMENTS
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.
Of those values found so far a(3n+2) > a(3n+1) by ~8%. - Robert G. Wilson v, Nov 03 2013
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
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..2560 (first 501 terms from T. D. Noe)
Mark Herkommer, Goldbach Conjecture Research.
Tomás Oliveira e Silva, Goldbach conjecture verification.
The Prime Glossary, Goldbach's conjecture
+Plus Magazine ... living mathematics, Mathematical mysteries: the Goldbach conjecture
Eric Weisstein's World of Mathematics, Goldbach Conjecture
Wikipedia, Goldbach conjecture
EXAMPLE
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.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Gilmar J. Rodriguez (Gilmar.Rodriguez(AT)nwfwmd.state.fl.us) and Robert G. Wilson v, Jun 16 2005
STATUS
approved