

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.


7



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
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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



