A134182 Difference between the sums of the first 10^n odd primes and the first 10^n odd positive integers > 1.

38, 14478, 2688838, 396250152, 52261798440, 6472980453364, 770530574266708, 89262852894258444, 10138479465982004008, 1134379338819040693132, 125436174619351016716668, 13738971133578180130155676, 1493061976858459711065006050, 161191473337955042966337346114

Offset: 1

Author

Enoch Haga, Oct 13 2007

Keywords

• nonn

Comments

Original name: 10^n-th difference between cumulative prime and odd sums.

Beginning at 3, compute the sums of the prime and odd sequences at 10^n and take the difference.

Examples

			a(1) = (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31) - (3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21) = 158 - 120 = 38.
a(2) = 14478 because at 10^2, 100 sums of primes and odds, the prime sum is 24678, the odd sum is 10200 and the difference is 14478.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..23 (using terms from A006988 and A099824)

Crossrefs

Cf. A006988, A071148, A005563, A099824, A134181.

Programs

UBASIC

10 N=1: A=2
20 A=nxtprm(A): B=B+A
30 N=N+2: D=D+N
40 if C=9 then print A;N;B;D;B-D: stop
50 C=C+1: if C<10 then 20

Formula

a(n) = A134181(10^n).

a(n) = A099824(n) + prime(10^n+1) - (10^n*(10^n+2)) - 2. - Chai Wah Wu, Mar 30 2020

a(n) = A071148(10^n) - (10^n+1)^2 + 1, where A071148 are the partial sums of odd primes, and N^2 is the sum of the first N odd integers. - M. F. Hasler, Aug 08 2025

Extensions

Edited by M. F. Hasler, Aug 08 2025