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A084697 a(1) = 2; for n >= 1, k>=1, a(n+1) = a(n) + k*n is the smallest such prime. 3

%I #29 Mar 18 2016 05:43:32

%S 2,3,5,11,19,29,41,83,107,179,199,331,367,419,433,463,479,547,601,677,

%T 757,883,971,1063,1087,1187,1213,1321,1433,1549,1579,1889,2017,2083,

%U 2287,2357,2393,2467,2543,2621,2741,3643,3727,4157,4201,4561,5021,5209

%N a(1) = 2; for n >= 1, k>=1, a(n+1) = a(n) + k*n is the smallest such prime.

%C Successive differences are 1,2,6,8,10,12,42,24,72,20,132,36,52,14,30,16,... and the n-th term is a multiple of n.

%C Conjecture: a(n) ~ c n^2 log(n) for some positive constant c. - _Robert Israel_, Oct 26 2015

%H Harvey P. Dale, <a href="/A084697/b084697.txt">Table of n, a(n) for n = 1..1000</a>

%H Zak Seidov, <a href="/A084697/a084697.png">Graph of first differences of A084697.</a>

%p a[1]:= 2: a[2]:= 3:

%p for n from 2 to 1000 do

%p if n::odd then delta:= 2*n

%p else delta:= n

%p fi:

%p for q from a[n] + delta by delta while not isprime(q) do od:

%p a[n+1]:= q

%p od:

%p seq(a[i],i=1..1000); # _Robert Israel_, Oct 26 2015

%t nxt[{n_,a_}]:=Module[{k=1},While[!PrimeQ[a+k*n],k++];{n+1,a+k*n}]; Transpose[NestList[nxt,{1,2},50]][[2]] (* _Harvey P. Dale_, Apr 11 2014 *)

%o (PARI) lista(nn) = {print1(a=2, ", "); for (n=1, nn, k=1; while (!isprime(na=a+k*n), k++); a = na; print1(a, ", "););} \\ _Michel Marcus_, Oct 21 2015

%K nonn

%O 1,1

%A _Amarnath Murthy_, Jun 05 2003

%E More terms from _David Wasserman_, Dec 30 2004

%E Definition corrected by _Zak Seidov_, Apr 24 2015

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)