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.

Showing 1-3 of 3 results.

A337249 Numbers k for which csc(k) > k.

Original entry on oeis.org

1, 3, 44, 710, 1420, 2130, 2840, 312689, 10838702, 6167950454, 21053343141, 63160029423, 105266715705
Offset: 1

Views

Author

Joseph C. Y. Wong, Aug 21 2020

Keywords

Comments

a(14) > 1.129*10^12, if it exists. - Kevin P. Thompson, Nov 07 2021
a(14) exists. The numbers 428224593349304, 6134899525417045, 66627445592888887, 430010946591069243, and 2646693125139304345 all satisfy csc(k) > k and are larger than a(13). It is not yet proven whether these are a(14) - a(18) or if there are any other numbers in the sequence before or between them. - Wolfe Padawer, Apr 11 2023

Examples

			csc(1) = 1.1884... so 1 is a term.

Crossrefs

Subsequence of A080142, A046955.
Subsequence of A265735 and A325158 if you omit the first term of A337249.
Cf. A092328, A337248.

Programs

  • Mathematica
    Select[Range[10^6], Csc[#] > # &] (* Amiram Eldar, Aug 21 2020 *)
  • PARI
    isok(m) = 1/sin(m) > m; \\ Michel Marcus, Aug 27 2020
  • Python
    import math
i = 1
while True:
  if 1 / math.sin(i) > i:
    print(i)
  i += 1

Extensions

a(11)-a(13) from Kevin P. Thompson, Nov 07 2021

A080157 Greedy frac multiples of gamma: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=gamma, where "frac(y)" denotes the fractional part of y.

Original entry on oeis.org

1, 2, 7, 9, 26, 52, 149, 272, 395, 790, 1185, 1580, 5653, 10911, 16169, 26685, 58628, 85313, 117256, 175884, 559595, 2179752, 5420066
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Examples

			a(3) = 7 since frac(1x) + frac(2x) + frac(7x) < 1, while frac(1x) + frac(2x) + frac(k*x) > 1 for all k>2 and k<7.

Crossrefs

Cf. A079938, A079939, A079940, A079941, A080142. Searching in the OEIS for "greedy frac" gives related sequences.

Programs

  • Maple
    Digits := 1000: a := []: s := 0: x := evalf(gamma): for n from 1 to 10000000 do: temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a),n]: print(n): s := s+evalf(frac(n*x)): fi: od: a;

A080158 Greedy frac multiples of Catalan's constant, G: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=G, where "frac(y)" denotes the fractional part of y.

Original entry on oeis.org

1, 11, 107, 10579, 21158, 53014, 106028, 625708, 721157, 1442314, 2163471, 2884628, 3605785, 4326942
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Comments

For definition of how the "Greedy Frac" sequence is defined, see other sequences in index.

Examples

			a(3) = 107 since frac(1x) + frac(11x) + frac(107x) < 1, while frac(1x) + frac(11x) + frac(k*x) > 1 for all k>11 and k<107.

Crossrefs

Cf. A079938, A079939, A079940, A079941, A080142, A080157.

Programs

  • Maple
    Digits := 1000: a := []: s := 0: x := evalf(Catalan): for n from 1 to 5000000 do: temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a),n]: print(n): s := s+evalf(frac(n*x)): fi: od: a;
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.