A078706 a(n) = smallest integer >=a(n-1) such that sum of first n terms is prime.

2, 3, 6, 6, 6, 6, 8, 10, 12, 12, 12, 14, 16, 18, 18, 18, 24, 32, 34, 36, 38, 42, 46, 48, 54, 56, 64, 68, 78, 90, 90, 94, 102, 114, 122, 124, 134, 144, 148, 150, 152, 160, 168, 170, 178, 182, 190, 192, 200, 216, 220, 222, 234, 234, 234, 246, 260, 264, 268, 270, 278, 280

Offset: 1

Author

Neil Fernandez, Dec 18 2002

Keywords

• easy
• nonn

Examples

			a(1)=2, the first prime. The smallest integer >=2 that yields a prime when added to 2 is 3, so a(2)=3. The smallest integer >=3 that yields a prime when added to 2+3 is 6 so a(3)=6.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051935.

Programs

Mathematica

s = 0; NestList[(s += #; NextPrime[s + # - 1] - s) &, 2, 61] (* Ivan Neretin, May 14 2015 *)
nxt[{t_,a_}]:=Module[{k=a},While[CompositeQ[t+k],k++];{t+k,k}]; NestList[nxt,{2,2},70][[;;,2]] (* Harvey P. Dale, Sep 01 2024 *)