A134182 -id:A134182 - cp's OEIS frontend

A134181 Difference between cumulative prime and odd sums.

0, 0, 0, 2, 4, 8, 12, 18, 28, 38, 52, 68, 84, 102, 124, 150, 176, 206, 238, 270, 306, 344, 386, 434, 484, 534, 586, 638, 692, 758, 826, 898, 970, 1050, 1130, 1214, 1302, 1392, 1486, 1584, 1682, 1788, 1894, 2002, 2110, 2228, 2356, 2486, 2616, 2748, 2884, 3020

Offset: 1

Enoch Haga, Oct 13 2007

This sequence is the difference between A071148 and A005563, as seen in the following tabular example: first column is prime, 2nd is odd, 3rd is prime sum (A071148), 4th is odd sum (A005563), 5th is the difference at each summation, the prime sequence increasingly greater.
3 3 3 0
5 8 8 0
7 15 15 0
9 26 24 2
11 39 35 4
13 56 48 8
15 75 63 12
17 98 80 18
19 127 99 28
21 158 120 38

			a(2)=0 because for the prime sequence beginning at 3, the sum is 8 (3+5). For the odd sequence beginning at 3 the sum is also 8 (3+5) and 8-8=0.

Cf. A071148, A005563, A134182.

lim=52;ps=Accumulate[Prime[Range[2,lim+1]]];os=Accumulate[Range[3,2lim+1,2]];ps-os (* James C. McMahon, Apr 05 2025 *)

10 N=1:A=2
20 A=nxtprm(A):B=B+A
30 N=N+2:D=D+N
40 print A;N;B;D;B-D:stop
50 C=C+1: if C<60 then 20

Beginning with 3 for both the prime and odd sequences, compute cumulative sums of both sequences and take the difference

cp's OEIS Frontend

A134181 Difference between cumulative prime and odd sums.

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