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 A093678 Sequence contains no 3-term arithmetic progression, starting with 1,7. 10
 1, 7, 8, 10, 11, 16, 17, 20, 28, 34, 35, 37, 38, 43, 44, 47, 82, 88, 89, 91, 92, 97, 98, 101, 109, 115, 116, 118, 119, 124, 125, 128, 244, 250, 251, 253, 254, 259, 260, 263, 271, 277, 278, 280, 281, 286, 287, 290, 325, 331, 332, 334, 335, 340, 341, 344, 352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(1)=1, a(2)=7; a(n) is least k such that no three terms of a(1),a(2),...,a(n-1),k form an arithmetic progression. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = sum[k=1, n-1, (3^A007814(k)+1)/2] + f(n), with f(n) an 8-periodic function with values {1, 6, 5, 6, 2, 6, 5, 7, ...}, as proved by Lawrence Sze. MAPLE N:= 1000: # to get all terms <= N V:= Vector(N, 1): A[1]:= 1: A[2]:= 7: k:= 8; for n from 3 while k < N do   for k from 1 to n-2 do     p:= 2*A[n-1]-A[k];     if p <= N then V[p]:= 0 fi   od:   for k from A[n-1]+1 to N do     if V[k] = 1 then A[n]:= k; nmax:= n; break fi;   od; od: seq(A[i], i=1..nmax); # Robert Israel, May 07 2018 CROSSREFS Cf. A004793, A033157, A093679-A093681, A092482. Row 3 of array in A093682. Sequence in context: A096677 A120192 A256651 * A188052 A266727 A214004 Adjacent sequences:  A093675 A093676 A093677 * A093679 A093680 A093681 KEYWORD nonn,look AUTHOR Ralf Stephan, Apr 09 2004 STATUS approved

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Last modified May 26 18:02 EDT 2018. Contains 304628 sequences. (Running on oeis4.)