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 1-2 of 2 results.

A216762 a(n) = n * ceiling(log_2(n)) * ceiling(log_2(log_2(n))) * ceiling(log_2(log_2(log_2(n)))) ....

Original entry on oeis.org

1, 2, 6, 8, 30, 36, 42, 48, 72, 80, 88, 96, 104, 112, 120, 128, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800
Offset: 1

Views

Author

Ken Takusagawa, Sep 15 2012

Keywords

Comments

a(n) is the product of n, ceiling(log_2(n)), ceiling(log_2(log_2(n))), ... with the base-2 logs iterated while the result remains greater than unity.
The sum of the reciprocals of a(n) diverge, but extremely slowly.
In particular, the sum of the reciprocals acts like lg* n asymptotically, where lg* x = 0 for x < 2 and lg* 2^x = 1 + lg* x. - Charles R Greathouse IV, Sep 25 2012

Examples

			a(0) is the product of 0 numbers, defined to be 1.
a(15) = 15 * ceiling(log_2(15)) * ceiling(log_2(log_2(15))) * ceiling(log_2(log_2(log_2(15)))) = 15 * 4 * 2 * 1 = 120.
a(17) = 17 * ceiling(log_2(17)) * ceiling(log_2(log_2(17))) * ceiling(log_2(log_2(log_2(17)))) * ceiling(log_2(log_2(log_2(log_2(17))))) = 17 * 5 * 3 * 2 * 1 = 510.

Crossrefs

Cf. A216761 (floor instead of ceiling).

Programs

  • Haskell
    a = product . map ceil . takeWhile (1<) . iterate log_2
  • Mathematica
    Table[prod = 1; s = n; While[s > 1, prod = prod*Ceiling[s]; s = Log[2, s]]; prod, {n, 50}] (* T. D. Noe, Sep 24 2012 *)
  • PARI
    a(n)=my(t=n);n-=1e-9;while(n>2,t*=ceil(n=log(n)/log(2)));t \\ Charles R Greathouse IV, Sep 25 2012

A232779 Sum of iterated logs; a(n) = 0 if n = 0; otherwise n + a(floor(log_2(n))).

Original entry on oeis.org

0, 1, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68
Offset: 0

Views

Author

Jeffrey Shallit, Nov 30 2013

Keywords

Examples

			a(5) = 5 + a(2) = 5 + 2 + a(1) = 5 + 2 + 1 + a(0) = 8.

Crossrefs

Cf. A216761.
Showing 1-2 of 2 results.

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