A127596 Numbers k such that 1 + Sum_{i=1..k-1} A001223(i)*(-1)^i = 0.

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

Offset: 1

Author

Manuel Valdivia, Apr 03 2007

Keywords

• nonn

Comments

Or, with prime(0) = 1, numbers k such that Sum_{i=0..k-1} (prime(i+1)-prime(i))*(-1)^i = Sum_{i=0..k-1} (A008578(i+1)-A008578(i))*(-1)^i = 0.

There are 313 terms < 10^7, 846 terms < 10^8, 1161 terms < 10^9.

Examples

			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.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..1161 (first 846 terms from Klaus Brockhaus)
• Eric Weisstein's World of Mathematics, Andrica's Conjecture
• Eric Weisstein's World of Mathematics, Prime Difference Function

Crossrefs

Cf. A001223 (differences between consecutive primes), A008578 (prime numbers at the beginning of the 20th century), A000101 (increasing gaps between primes, upper end), A002386 (increasing gaps between primes, lower end).

Cf. A282178 (prime(a(n))), A330545, A330547.

Programs

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}]

PARI

{m=10^8; n=1; p=1; e=1; s=0; while(nKlaus Brockhaus, Apr 29 2007 */

Extensions

Edited by Klaus Brockhaus, Apr 29 2007