A064455 -id:A064455 - cp's OEIS frontend

A162888 An alternating sum of the first n nonprimes.

1, 3, 3, 4, 5, 15, 6, 7, 8, 24, 9, 10, 11, 33, 12, 13, 39, 14, 42, 15, 16, 17, 51, 18, 54, 19, 20, 60, 21, 22, 23, 69, 24, 25, 75, 26, 78, 27, 28, 84, 29, 87, 30, 31, 32, 96, 33, 99, 34, 35, 105, 36, 37, 38, 114, 39, 117, 40, 41, 123, 42, 43, 129, 44, 132, 45, 46, 138, 47, 141

Offset: 1

Juri-Stepan Gerasimov, Jul 16 2009

nonn

Define an alternating 1-based sum S(n) = (1-0)+(1+1)+(1-2)+...(1-(-1)^n*n) = A064455(n+1).

The sequence evaluates this sum for an upper limit of the n-th nonprime A141468(n).

			a(1) = 1 = 1 - (-1)^0*0.
a(2) = 3 = 1 - (-1)^0*0 + 1 -(-1)^1*1.
a(3) = 3 = 1 - (-1)^0*0 + 1 -(-1)^1*1 + 1 - (-2)^2*2 + 1 - (-1)^3*3 + 1 - (-1)^4*4.

Cf. A064455, A141468.

A141468 := proc(n) option remember; local a; if n = 1 then 0 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
A064455 := proc(n) if type(n,'even') then 3*n/2; else (n+1)/2 ; fi; end:
A162888 := proc(n) A064455(A141468(n)+1) ; end: seq(A162888(n),n=1..100) ; # R. J. Mathar, Jul 19 2009

a(n) = A064455(A141468(n)+1). - R. J. Mathar, Jul 19 2009

Definition edited by R. J. Mathar, Jul 19 2009

A162887 Odd nonprimes in an alternating 1-based sum up to some odd nonprime.

Original entry on oeis.org

15, 33, 39, 51, 69, 75, 87, 105, 117, 123, 129, 141, 159, 177, 183, 189, 195, 201, 213, 219, 231, 243, 249, 255, 267, 279, 285, 303, 309, 315, 321, 327, 333, 339, 357, 369, 375, 381, 393, 399, 411, 429, 435, 447, 453, 459, 465, 483, 489, 495, 501, 513, 519

Offset: 1

Juri-Stepan Gerasimov, Jul 16 2009

Define the alternating sum S(u) = sum_{k=0..u} (1-(-1)^k*k) = A064455(u+1) as in A162886.

Evaluate the sum with upper limits u= 1,9, 15, 21... from A014076, and add S(u) to this sequence here whenever it is itself a member of A014076.

			The sequence S(u) = 3, 15, 24, 33, 39, 42, 51, 54, 60, 69, ... is generated by u = 1, 9, 15, 21, ...
The first S-term, 3, is prime, and therefore not added to the sequence. The second S-term, 15, is an odd nonprime and added to the sequence. The third, 24, is even and not added to the sequence.

Cf. A014076.

3 removed by R. J. Mathar, Aug 27 2009

cp's OEIS Frontend

A162888 An alternating sum of the first n nonprimes.

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