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.

A029920 Convert n from centimeters (cm) to inches (").

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 8.

Links

Crossrefs

Cf. A085269 (with floor), A029919.

Programs

A332102 Least m > 0 such that 2*m^n <= Sum_{k < m} k^n.

Original entry on oeis.org

3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 55, 57, 60, 62, 65, 67, 70, 72, 75, 77, 79, 82, 84, 87, 89, 92, 94, 97, 99, 102, 104, 107, 109, 112, 114, 116, 119, 121, 124, 126, 129, 131, 134, 136, 139, 141, 144, 146, 149, 151, 153, 156, 158, 161, 163, 166
Offset: 0

Views

Author

M. F. Hasler, Apr 18 2020

Keywords

Comments

Obviously a(n) is a lower limit for any s solution to 2*s^n = Sum_{x in S} x^n, S subset of {1, ..., s-1}.
First differences are (2, 3, 2, 3, ...) except for a duplicated 2 in positions {16, 31, 46, 61, 76, 91; 104, 119, 134, 149, 164, 179, 194, 209, 224, 239, 254, 269; 282, 297, ...}: Here the first differences are always 15 except for a 13 after the 6th, 18th, ... term.

Examples

			For n=0, 2*m^0 = 2 > Sum_{k<m} k^0 = m - 1 <=> 3 > m, so a(0) = 3.
For n=1, 2*m^1 > Sum_{k<m} k^1 = m(m-1)/2 <=> 4 > m - 1, so a(1) = 5.

Crossrefs

Cf. A332101 (same without factor 2 in definition).
Cf. A195168, A047218, A029919 (all have common initial terms but differ later and only remain lower resp. upper bounds).

Programs

  • Mathematica
    Table[Block[{m = 1, s = 0}, While[2 m^n > s, s = s + m^n; m++]; m], {n, 0, 66}] (* Michael De Vlieger, Apr 30 2020 *)
  • PARI
    apply( A332102(n, s)=for(m=1, oo, s<2*m^n||return(m); s+=m^n), [0..66])

Formula

a(n) >= A195168(n+1) with equality for n not in {13, 15; 26, 28, 30; 39, 41, 43, 45; 52, 54, ..., 60; 65, 67, ..., 75, 78, 80, ..., 90; 89, 91, ..., 103; 102, 104, ..., 114, 115, ...} \ {120, 122, 124, 126, 135, 137, 139, 150, 152, 165}.
a(n) <= A047218(n+2) with equality for n <= 17 and even n <= 34.
Conjecture: a(n) = round(n/log(3/2) + 3).

A220000 Sixty fourths of an inch in thousandths, rounded to nearest integer.

Original entry on oeis.org

16, 31, 47, 63, 78, 94, 109, 125, 141, 156, 172, 188, 203, 219, 234, 250, 266, 281, 297, 313, 328, 344, 359, 375, 391, 406, 422, 438, 453, 469, 484, 500, 516, 531, 547, 563, 578, 594, 609, 625, 641, 656, 672, 688, 703, 719, 734, 750, 766, 781
Offset: 1

Views

Author

Marc Alan Rosner, Dec 03 2012

Keywords

Comments

Diameter of successive drill bits, in thousandths of an inch, within an ordered set consisting of increments of 1/64th of an inch. Traditionally the sizes of bits in such a set are expressed in simplest reduced fractional inch values: 1/64, 1/32, 3/64, 1/16, etc. Of fundamental importance to machinists, tool and die makers, carpenters, hobbyists, insomnial science teachers, etc.

Examples

			For n = 5 the a(5) term = (5/64)*1000 = 78.125, which is rounded to 78.

References

  • Jack Erjavec, Automotive Technology, 2010, pages 66-73.
  • Frank D. Graham, Audels Machinists and Tool Makers Handy Book, 1941, pages 34-48.
  • IBM Corp., Precision Measurement in the Metal Working Industry, 1939, page 11.

Links

Crossrefs

Cf. A085269, A029919, A029920, A169860, A169861.

Programs

Formula

a(n) = round(125*n/8), with 0.5 rounded up.
Showing 1-3 of 3 results.

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

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