A082455 -id:A082455 - cp's OEIS frontend

A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.

0, 0, 5, 3, 9, 9, 15, 15, 21, 21, 31, 29, 39, 39, 45, 45, 55, 57, 63, 65, 73, 71, 81, 81, 91, 95, 103, 101, 109, 107, 115, 125, 133, 135, 141, 147, 153, 155, 165, 165, 175, 177, 183, 189, 195, 195, 201, 209, 225, 225, 231, 231, 241, 239, 253, 255, 265, 267, 273, 275

Offset: 0

Labos Elemer, Apr 25 2003

nonn

In fact only one initial value is needed.
If initial values were {a(0)=0, a(1)=1} then we would get A014687.
prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 31 + 29 (order was reversed!).
If initial values were {a(0)=1, a(1)=2} then (after a(0)=1) we would get A000040, the primes, and would have prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 29 + 31 (identity).
Initial values {a(0)=1, a(1)=3} would give A014686.

Cf. A000040, A014686, A014687, A082455.

g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=0; Table[g[w], {w, 0, 100}]
Prepend[Table[Prime[n] + 2 (-1)^n, {n, 59}],0] (* George Beck, Jun 03 2022 *)

lista(nn) = {print1(a=0, ", "); print1(a, ", "); for (n=2, nn, a = prime(n) + prime(n-1) - a; print1(a, ", "););} \\ Michel Marcus, Apr 06 2015

a(n) = prime(n) + 2*(-1)^n. - George Beck, Jun 03 2022

Name corrected by George Beck, Jun 03 2022

A082456 a(n) = prime(n) + prime(n-1) - a(n-1), with a(0)=0, a(1)=127, and prime(i) is the i-th prime.

Original entry on oeis.org

0, 127, -122, 130, -118, 136, -112, 142, -106, 148, -96, 156, -88, 166, -82, 172, -72, 184, -64, 192, -54, 198, -46, 208, -36, 222, -24, 228, -18, 234, -12, 252, 6, 262, 14, 274, 26, 282, 38, 292, 48, 304, 56, 316, 68, 322, 74, 336, 98, 352, 104, 358, 114, 366, 126, 382, 138, 394, 146, 402, 156, 408, 168, 432, 186, 438

Offset: 0

Labos Elemer, Apr 25 2003

sign

Initial values {0, 1} give A014687.
Initial values {1, 2} give A000040.
Initial values {1, 3} give A014686.

Cf. A000040, A014686, A014687, A082454, A082455.

g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=127; Table[g[w], {w, 0, 100}]

a(n) = if (n==0, 0, if (n==1, 127, prime(n) + prime(n-1) - a(n-1))); \\ Michel Marcus, Mar 08 2022

Entry revised by N. J. A. Sloane, Dec 22 2005

cp's OEIS Frontend

A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.

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