A082974 a(n) = (a(n-1) + p(n)) mod p(n+1).

2, 0, 5, 1, 12, 8, 6, 2, 25, 23, 17, 13, 11, 7, 1, 54, 52, 46, 42, 40, 34, 30, 24, 16, 12, 10, 6, 4, 0, 113, 109, 103, 101, 91, 89, 83, 77, 73, 67, 61, 59, 49, 47, 43, 41, 29, 17, 13, 11, 7, 1, 240, 230, 224, 218, 212, 210, 204, 200, 198, 188, 174, 170, 168, 164, 150, 144, 134

Offset: 1

Author

Jon Perry, May 28 2003

Keywords

• nonn
• easy

Comments

Differences when decreasing are essentially A001223, so increases occur when primes being used are roughly double those at previous increase; e.g. a(3352)=(12+31123)mod 31139=31135 and a(6257)=(1+62273)mod 62297=62274 - Henry Bottomley, Jul 13 2003

Examples

			a(2) = (a(1) + 3) mod 5 = 5 mod 5 = 0.
a(3) = (a(2) + 5) mod 7 = 5 mod 7 = 5.
a(4) = (a(3) + 7) mod 11 = 12 mod 11 = 1.
		

Links

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

Crossrefs

Cf. A000040, A001223, A071089.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,Mod[a+Prime[n+1],Prime[n+2]]}; NestList[nxt,{1,2},70][[All,2]] (* Harvey P. Dale, Sep 13 2016 *)

PARI

ps=0; pc=1; while (pc<100,ps+=prime(pc); ps%=prime(pc++); print1(ps","))

Extensions

Edited by Henry Bottomley, Jul 13 2003

Definition clarified by Harvey P. Dale, Sep 13 2016