A106738 Difference between the sums of odd-indexed primes and even-indexed primes up to and including index 10^n.

13, 251, 4031, 52017, 652039, 7746369, 89721621, 1019145113, 11401770915, 126048548239

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = Sum2 - Sum1, where Sum1 = prime(1) + prime(3) + ... + prime(10^n-1), and Sum2 = prime(2) + prime(4) + ... + prime(10^n).

a(n) = Sum_{i=1..10^n} (-1)^i*A000040(i). - R. J. Mathar, Feb 13 2008

a(n) = A077133(10^n/2). - Amiram Eldar, Jul 02 2024

Maple

A106738 := proc(n) local a, i ; a :=0 ; for i from 1 to 10^n do a := a+(-1)^i*ithprime(i) ; od: RETURN(a) ; end: for n from 1 do print(A106738(n)) ; od: # R. J. Mathar, Feb 13 2008

Mathematica

a[n_] := Module[{a = 0}, For[i = 1, i <= 10^n, i++, a = a + (-1)^i*Prime[i]]; a]; Table[Print[an = a[n]]; an, {n, 1, 8}] (* Jean-François Alcover, Dec 17 2012, after R. J. Mathar *)

Prog

(PARI) lista(pmax) = {my(pow = 10, k = 0, s = 0); forprime(p = 1, pmax, k++; s += ((-1)^k * p); if(k == pow, print1(s, ", "); pow *= 10)); } \\ Amiram Eldar, Jul 02 2024

Crossrefs

Cf. A000040, A031215, A031368, A077126, A077131, A077133.

Sequence in context: A183416 A126422 A286878 * A332849 A001508 A157946

Adjacent sequences: A106735 A106736 A106737 * A106739 A106740 A106741

Keyword

nonn,more

Author

Cino Hilliard, May 15 2005

Extensions

Edited by R. J. Mathar, Feb 13 2008

a(7)-a(8) from Donovan Johnson, Nov 30 2008

a(9)-a(10) from Amiram Eldar, Jul 02 2024

Status

approved