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 A004793 a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression. 18
 1, 3, 4, 6, 10, 12, 13, 15, 28, 30, 31, 33, 37, 39, 40, 42, 82, 84, 85, 87, 91, 93, 94, 96, 109, 111, 112, 114, 118, 120, 121, 123, 244, 246, 247, 249, 253, 255, 256, 258, 271, 273, 274, 276, 280, 282, 283, 285, 325, 327, 328, 330, 334, 336, 337, 339, 352, 354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sci. 16E, 237-240, 1997. Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence FORMULA a(n) = (3-n)/2 + 2*floor(n/2) + sum(k=1, n-1, 3^A007814(k))/2 = A003278(n) + [n is even], proved by Lawrence Sze, following a conjecture by Ralf Stephan. a(n) = b(n-1), with b(0)=1, b(2n)=3b(n)-2-3[n odd], b(2n+1)=3b(n)-3[n odd]. MATHEMATICA Select[Range[1000], MatchQ[IntegerDigits[#-1, 3], {(0|1)..., 0|2}]&] (* Jean-François Alcover, Jan 13 2019, after Tanya Khovanova in A186776 *) PROG (PARI) v[1]=1; v[2]=3; for(n=3, 1000, f=2; m=v[n-1]+1; while(1, forstep(k=n-1, 1, -1, if(v[k]<(m+1)/2, f=1; break); for(l=1, k-1, if(m-v[k]==v[k]-v[l], f=0; break)); if(f<2, break)); if(!f, m=m+1; f=2); if(f==1, break)); v[n]=m) \\ Ralf Stephan (PARI) a(n)=if(n<1, 1, if(n%2==0, 3*a(n/2)-2-3*((n/2)%2), 3*a((n-1)/2)-3*(((n-1)/2)%2))) \\ Ralf Stephan CROSSREFS Equals A186776(n)+1, A033160(n)-1, A033163(n)-2. Cf. A092482, A185256. Row 1 of array in A093682. Sequence in context: A322457 A137951 A082694 * A031132 A322165 A057477 Adjacent sequences:  A004790 A004791 A004792 * A004794 A004795 A004796 KEYWORD nonn,changed AUTHOR EXTENSIONS Rechecked by David W. Wilson, Jun 04 2002 STATUS approved

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Last modified January 16 00:02 EST 2019. Contains 319184 sequences. (Running on oeis4.)