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

0,3

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A073627.

Sequence in context: A169743 A191986 A018699 * A067938 A306073 A018457

Adjacent sequences: A073625 A073626 A073627 * A073629 A073630 A073631

Keyword

nonn

Author

Amarnath Murthy, Aug 08 2002

Extensions

More terms from Matthew Conroy, Sep 09 2002

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

Status

approved