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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)