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 A093682 Array T(m,n) by antidiagonals: nonarithmetic-3-progression sequences with simple closed forms. 15
 1, 2, 1, 4, 3, 1, 5, 4, 4, 1, 10, 6, 5, 7, 1, 11, 10, 8, 8, 10, 1, 13, 12, 10, 10, 11, 19, 1, 14, 13, 13, 11, 13, 20, 28, 1, 28, 15, 14, 16, 14, 22, 29, 55, 1, 29, 28, 17, 17, 20, 23, 31, 56, 82, 1, 31, 30, 28, 20, 22, 28, 32, 58, 83, 163, 1, 32, 31, 31, 28, 23, 29, 37, 59, 85 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The nonarithmetic-3-progression sequences starting with a(1)=1, a(2)=1+3^m or 1+2*3^m, m>=0, seem to have especially simple 'closed' forms. None of these formulas have been proved, however. T(m,1)=1, T(m,2) = 1+(1+[m even])*3^[m/2] = 1+A038754(m), m>=0, n>0; T(m,n) is least k such that no three terms of T(m,1),T(m,2),...,T(m,n-1),k form an arithmetic progression. LINKS Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence. FORMULA T(m, n) = sum[k=1, n-1, (3^A007814(k)+1)/2] + f(n), with f(n) a P-periodic function, where P <= 2^[(m+3)/2] (conjectured and checked up to m=13, n=1000). The formula implies that T(m, n)=b(n-1) where b(2n)=3b(n)+p(n), b(2n+1)=3b(n)+q(n), with p, q sequences generated by rational o.g.f.s. EXAMPLE 1 2 4 5 10 11 13 ... 1 3 4 6 10 12 13 ... 1 4 5 8 10 13 14 ... 1 7 8 10 11 16 17 ... 1 10 11 13 14 20 22 ... CROSSREFS Rows 0-6 are A003278, A004793, A033157, A093678, A093679, A093680, A093681. Column 2 is 1+A038754. Cf. A092482, A033158. Sequence in context: A265624 A332332 A335259 * A344767 A187883 A134543 Adjacent sequences:  A093679 A093680 A093681 * A093683 A093684 A093685 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Apr 09 2004 STATUS approved

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Last modified June 18 13:21 EDT 2021. Contains 345112 sequences. (Running on oeis4.)