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

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

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