

A093678


Sequence contains no 3term 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
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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(n1),k form an arithmetic progression.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries related to nonaveraging sequences


FORMULA

a(n) = sum[k=1, n1, (3^A007814(k)+1)/2] + f(n), with f(n) an 8periodic 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 n2 do
p:= 2*A[n1]A[k];
if p <= N then V[p]:= 0 fi
od:
for k from A[n1]+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, A093679A093681, 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



