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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
2, 3, 5, 11, 19, 29, 41, 83, 107, 179, 199, 331, 367, 419, 433, 463, 479, 547, 601, 677, 757, 883, 971, 1063, 1087, 1187, 1213, 1321, 1433, 1549, 1579, 1889, 2017, 2083, 2287, 2357, 2393, 2467, 2543, 2621, 2741, 3643, 3727, 4157, 4201, 4561, 5021, 5209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

Conjecture: a(n) ~ c n^2 log(n) for some positive constant c. - Robert Israel, Oct 26 2015

LINKS

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

Zak Seidov, Graph of first differences of A084697.

MAPLE

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

for n from 2 to 1000 do

   if n::odd then delta:= 2*n

   else delta:= n

   fi:

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

   a[n+1]:= q

od:

seq(a[i], i=1..1000); # Robert Israel, Oct 26 2015

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A087582 A235661 A070865 * A037082 A084573 A155954

Adjacent sequences:  A084694 A084695 A084696 * A084698 A084699 A084700

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 05 2003

EXTENSIONS

More terms from David Wasserman, Dec 30 2004

Definition corrected by Zak Seidov, Apr 24 2015

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)