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A083236 First order recursion: a(0)=2; a(n) = prime(n) - a(n-1). 5
0, 3, 2, 5, 6, 7, 10, 9, 14, 15, 16, 21, 20, 23, 24, 29, 30, 31, 36, 35, 38, 41, 42, 47, 50, 51, 52, 55, 54, 59, 68, 63, 74, 65, 84, 67, 90, 73, 94, 79, 100, 81, 110, 83, 114, 85, 126, 97, 130, 99, 134, 105, 136, 115, 142, 121, 148, 123, 154, 127, 156, 137, 170, 141, 172, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Observe relationship: a(n-1) + a(n) = prime(n), the n-th prime;

n=6: a(6)+a(7) = 7+10 = prime(7) = 17 and a(7)+a(8) = 10+9 = 19 = prime(8);

It follows also that a(n+1)-a(n-1) = A001223(n).

LINKS

Table of n, a(n) for n=1..66.

MATHEMATICA

RecursionLimit$=10000; f[x_] := Prime[x]-f[x-1]; f[0]=2; Table[f[w], {w, 1, 100}]

Join[{0}, Abs[Accumulate[Table[Prime[n](-1)^n, {n, 2, 70}]]]] (* Harvey P. Dale, Nov 20 2013 *)

PROG

(PARI) lista(nn) = {my(last = 2, new, v=vector(nn)); for (n=1, nn, v[n] = prime(n) - last; last = v[n]; ); v; } \\ Michel Marcus, Mar 27 2020

CROSSREFS

Cf. A000040, A001223.

Sequence in context: A305428 A269376 A257793 * A302717 A277820 A277680

Adjacent sequences:  A083233 A083234 A083235 * A083237 A083238 A083239

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 23 2003

STATUS

approved

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Last modified May 25 17:53 EDT 2020. Contains 334595 sequences. (Running on oeis4.)