A073628 a(0) = 0; a(1) = 1; a(2) = 2; a(n) = smallest number greater than the previous term such that the sum of three successive terms is a prime.

0, 1, 2, 4, 5, 8, 10, 11, 16, 20, 23, 24, 26, 29, 34, 38, 41, 48, 50, 51, 56, 60, 63, 68, 80, 81, 90, 92, 95, 96, 102, 109, 120, 124, 129, 130, 138, 141, 142, 148, 149, 152, 156, 159, 164, 168, 171, 182, 188, 193, 196, 198, 199, 202, 206, 209, 216, 218, 219, 222, 232

Offset: 0

Author

Amarnath Murthy, Aug 08 2002

Keywords

• nonn

Comments

Slowest increasing sequence where 3 consecutive integers sum up to a prime.

In a string there can be at most two consecutive integers, e.g., (10, 11). More generally, three consecutive terms cannot be in arithmetic progression.

Examples

			0 + 1 + 2 = 3, which is prime; 1 + 2 + 4 = 7, which is prime; 2 + 4 + 5 = 11, which is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A073627.

Programs

Mathematica

n1 = 0; n2 = 1; counter = 1; maxnumber = 10^4; Do[ If[PrimeQ[n1 + n2 + n], {sol[counter] = n; counter = counter + 1; n1 = n2; n2 = n}], {n, 2, maxnumber}]; Table[sol[j], {j, 1, counter}] (* Ben Ross (bmr180(AT)psu.edu), Jan 29 2006 *)
nxt[{a_,b_,c_}]:={b,c,Module[{x=c+1},While[!PrimeQ[b+c+x],x++];x]}; Transpose[ NestList[nxt,{0,1,2},60]][[1]] (* Harvey P. Dale, Jun 10 2013 *)

Extensions

More terms from Matthew Conroy, Sep 09 2002

Entry revised by N. J. A. Sloane, Mar 25 2007