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A082974
a(n) = (a(n-1) + p(n)) mod p(n+1).
2
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
1,1
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
LINKS
EXAMPLE
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.
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 *)
PROG
(PARI) ps=0; pc=1; while (pc<100, ps+=prime(pc); ps%=prime(pc++); print1(ps", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, May 28 2003
EXTENSIONS
Edited by Henry Bottomley, Jul 13 2003
Definition clarified by Harvey P. Dale, Sep 13 2016
STATUS
approved