A131733 -id:A131733 - cp's OEIS frontend

A108754 Difference between partial sum of the first n primes and n^2.

1, 1, 1, 1, 3, 5, 9, 13, 19, 29, 39, 53, 69, 85, 103, 125, 151, 177, 207, 239, 271, 307, 345, 387, 435, 485, 535, 587, 639, 693, 759, 827, 899, 971, 1051, 1131, 1215, 1303, 1393, 1487, 1585, 1683, 1789, 1895, 2003, 2111, 2229, 2357, 2487, 2617, 2749, 2885, 3021

Offset: 1

Alexandre Wajnberg, Jun 23 2005

Also difference between partial sum of the first n primes and the sum of the first n odd numbers. - Cino Hilliard, Dec 02 2007

			a(5) = A007504(5) - A000290(5) = 28 - (5^2) = 3.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000290, A007504.

Partial sums of A131733.

Table[ Sum[ Prime[i], {i, n}] - n^2, {n, 53}] (* Robert G. Wilson v, Jun 25 2005 *)
Module[{nn=60,prs},prs=Accumulate[Prime[Range[nn]]];#[[1]]-#[[2]]&/@Thread[ {prs,Range[ nn]^2}]] (* Harvey P. Dale, Aug 14 2024 *)

g(n) = for(x=1,n,y=sum(j=1,x,2*j-1);z=sum(j=1,x,prime(j));print1(z-y",")) \\ Cino Hilliard, Dec 02 2007

a(n) = A007504(n) - A000290(n).

Edited and extended by Robert G. Wilson v, Jun 25 2005

A192326 Remainders of primes divided by odd numbers.

Original entry on oeis.org

0, 0, 0, 0, 2, 2, 4, 4, 6, 10, 10, 14, 16, 16, 18, 22, 26, 26, 30, 32, 32, 36, 38, 42, 48, 50, 50, 52, 52, 54, 5, 5, 7, 5, 11, 9, 11, 13, 13, 15, 17, 15, 21, 19, 19, 17, 25, 33, 33, 31, 31, 33, 31, 37, 39, 41, 43, 41, 43, 43, 41, 47, 57, 57, 55, 55, 65, 67, 73, 71, 71, 73, 77, 79, 81, 81, 83

Offset: 1

Pasi Airikka, Jun 28 2011

			a(1) = prime(1) mod odd(1) = 2 mod 1 = 0; a(5) = prime(5) mod odd(5) = 11 mod 9 = 2.

Cf. A131733.

% n = number of computed terms of sequence
for i=1:n,
    a(n) = mod(prime(i),odd(i)) ;
end

A192326 := proc(n) modp(ithprime(n),2*n-1) ; end proc:
seq(A192326(n),n=1..80) ; # R. J. Mathar, Jul 13 2011

a(n)=prime(n)%(2*n-1) \\ Charles R Greathouse IV, Jun 29 2011

a(n) = prime(n) mod (2n-1).

cp's OEIS Frontend

A108754 Difference between partial sum of the first n primes and n^2.

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