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 A105822 For n > 2, a(n) > 0 not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) = d^2 is a minimal square, a(1)=1, a(2)=2. 14
 1, 2, 3, 5, 8, 4, 12, 7, 10, 17, 6, 11, 21, 32, 13, 19, 14, 33, 20, 28, 24, 27, 42, 40, 18, 9, 35, 44, 39, 54, 48, 22, 15, 37, 52, 89, 30, 59, 23, 36, 99, 70, 16, 86, 47, 45, 92, 65, 157, 34, 123, 135, 222, 56, 136, 82, 29, 53, 102, 155, 25, 130, 87, 43, 170, 213, 63, 150, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Is it a permutation of positive integers? Among first 2000 terms, first missing numbers are 233, 349, 394, 443, 449. The sequence depends on seed terms a(1) and a(2); if a(1) = 1, a(3) = a(2)+1. Values of d^2 in A105823. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 MAPLE N:= 1000: # to get a(1) to a(N) S:= 'S': a[1]:= 1: a[2]:= 2: S[1]:= 1: S[2]:= 1: for n from 3 to N do ds:= map(t -> rhs(op(t)), [msolve(x^2=a[n-1]^2, 4*a[n-2])]); xmin:= infinity; for d in ds do found:= false; for y from floor((a[n-1]-d)/(4*a[n-2]))+1 do xy:= 4*a[n-2]*y + d; cand:= (xy^2 - a[n-1]^2)/(4*a[n-2]); if cand >= xmin then found:= false; break fi; if not assigned(S[cand]) then found:= true; break fi; od: if found then xmin:= cand; fi; od: a[n]:= xmin; S[xmin]:= 1; od: seq(a[n], n=1..N); # Robert Israel, May 11 2015 MATHEMATICA a = {1, 2}; Do[i = 1; While[MemberQ[a, i] || !IntegerQ[Sqrt[a[[-1]]^2 + 4 a[[-2]]*i]], i++]; AppendTo[a, i], {n, 3, 70}]; a (* Ivan Neretin, May 11 2015 *) CROSSREFS Cf. A076839, A105823, A104663 (putative inverse). Sequence in context: A122597 A323890 A105836 * A191543 A191455 A191540 Adjacent sequences: A105819 A105820 A105821 * A105823 A105824 A105825 KEYWORD nonn AUTHOR Zak Seidov, Apr 22 2005 STATUS approved

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Last modified September 14 21:48 EDT 2024. Contains 375929 sequences. (Running on oeis4.)