cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A023184 Least Fibonacci number ending with n.

Original entry on oeis.org

0, 1, 2, 3, 34, 5, 10946, 377, 8, 89, 610, 17711, 619220451666590135228675387863297874269396512, 13, 70492524767089125814114, 659034621587630041982498215, 57602132235424755886206198685365216, 24157817, 196418, 114059301025943970552219, 1548008755920
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

The Fibonacci index of the 12th to 25th terms respectively are 216, 7, 111, 130, 168, 37, 27, 112, 90, 8, 183, 286, 252 and 25.

Examples

			a(11) = 17711 is the smallest Fibonacci number ending in 11.

Crossrefs

Cf. A000045, A023185, A020344, A020345.

Programs

  • Maple
    with(combinat):for n from 1 to 40 do e := 1; g := ceil(log(n+1)/log(10)-0.00001): while((fibonacci(e) mod 10^g)n) do e := e+1:end do: q[n] := fibonacci(e):end do:seq(q[i],i=1..40);
  • Mathematica
    d[n_]:=IntegerDigits[n]; Table[j=0; While[Length[d[Fibonacci[j]]]<(le=Length[y=d[n]]), j++]; i=j; While[Take[d[x=Fibonacci[i]],-le]!=y,i++]; x,{n,0,20}] (* Jayanta Basu, May 18 2013 *)

A297327 1/36 of the square of the basis of a primitive 3-simplex.

Original entry on oeis.org

6434041, 89002225, 865125625, 89610625, 353440516, 29160156025, 18989880481, 37434450625, 72399370000, 444515646025, 346008660625, 2003915162500, 9475360381201, 166729268761, 13110591519025, 8007417968121, 11201866562500, 3095696620900, 61956758281561
Offset: 1

Views

Author

Ralf Steiner, Dec 28 2017

Keywords

Comments

For every primitive trirectangular tetrahedron (0, a, b, c) with coprime integer sides, (b*c)^2 + (a*b)^2 + (c*a)^2 is divisible by 144.
The square of the basis is related by De Gua's theorem on the square of the main diagonal of a (different, not necessarily primitive) Euler brick (a*b/12=A031173(k), a*c/12=A031174(k), b*c/12=A031175(k)) also having integer sides and integer face diagonals including a trirectangular tetrahedron (0, a*b/12, a*c/12, b*c/12), such as a(1) = 6434041 = A023185(8) = A031173(8)^2 + A031174(8)^2 + A031175(8)^2.
By this process a cycle of primitive trirectangular tetrahedrons is defined, such as with indices k: (1 8), (2 6), (3 5), (4 7), (9 19), ...

Links

Crossrefs

Cf. A295507, A023185, A031173, A031174, A031175.

Formula

a(n) = (1/144)*(A031174(n)^2*A031175(n)^2 + A031173(n)^2*(A031174(n)^2 + A031175(n)^2)).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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