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 A127596 Numbers k such that 1 + Sum_{i=1..k-1} A001223(i)*(-1)^i = 0. 6
 2, 4, 14, 22, 28, 233, 249, 261, 488, 497, 511, 515, 519, 526, 531, 534, 548, 562, 620, 633, 635, 2985, 3119, 3123, 3128, 3157, 4350, 4358, 4392, 4438, 4474, 4484, 4606, 4610, 4759, 5191, 12493, 1761067, 2785124, 2785152, 2785718, 2785729, 2867471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or, with prime(0) = 1, numbers n such that Sum{k=0..n-1} (prime(k+1)-prime(k))*(-1)^k = Sum{k=0..n-1} (A008578(k+1)-A008578(k))*(-1)^k = 0. There are 313 terms < 10^7, 846 terms < 10^8, 1161 terms < 10^9. LINKS Eric Weisstein's World of Mathematics, Andrica's Conjecture Eric Weisstein's World of Mathematics, Prime Difference Function EXAMPLE 1 - A001223(1) = 1 - 1 = 0, hence 2 is a term. 1 - A001223(1) + A001223(2) - A001223(3) = 1 - 1 + 2 - 2 = 0, hence 4 is a term. MATHEMATICA S=0; Do[j=Prime[n+1]; i=Prime[n]; d[n]=j-i; S=S+(d[n]*(-1)^n); If[S+1==0, Print[Table[j|PrimePi[j]|S+1]]], {n, 1, 10^7, 1}] PROG (PARI) {m=10^8; n=1; p=1; e=1; s=0; while(n

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Last modified October 20 22:22 EDT 2021. Contains 348119 sequences. (Running on oeis4.)