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

%I A134182 #26 Aug 09 2025 11:24:16
%S A134182 38,14478,2688838,396250152,52261798440,6472980453364,770530574266708,
%T A134182 89262852894258444,10138479465982004008,1134379338819040693132,
%U A134182 125436174619351016716668,13738971133578180130155676,1493061976858459711065006050,161191473337955042966337346114
%N A134182 Difference between the sums of the first 10^n odd primes and the first 10^n odd positive integers > 1.
%C A134182 Original name: 10^n-th difference between cumulative prime and odd sums.
%C A134182 Beginning at 3, compute the sums of the prime and odd sequences at 10^n and take the difference.
%H A134182 Chai Wah Wu, <a href="/A134182/b134182.txt">Table of n, a(n) for n = 1..23</a> (using terms from A006988 and A099824)
%F A134182 a(n) = A134181(10^n).
%F A134182 a(n) = A099824(n) + prime(10^n+1) - (10^n*(10^n+2)) - 2. - _Chai Wah Wu_, Mar 30 2020
%F A134182 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
%e A134182 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.
%e A134182 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.
%o A134182 (UBASIC)
%o A134182 10 N=1: A=2
%o A134182 20 A=nxtprm(A): B=B+A
%o A134182 30 N=N+2: D=D+N
%o A134182 40 if C=9 then print A;N;B;D;B-D: stop
%o A134182 50 C=C+1: if C<10 then 20
%Y A134182 Cf. A006988, A071148, A005563, A099824, A134181.
%K A134182 nonn
%O A134182 1,1
%A A134182 _Enoch Haga_, Oct 13 2007
%E A134182 Edited by _M. F. Hasler_, Aug 08 2025