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.

User: Jake Baron

Jake Baron's wiki page.

Jake Baron has authored 5 sequences.

A268541 Base in which the Fouriest transform of A268540(n) is 44.

Original entry on oeis.org

5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 31, 32, 34, 37, 38, 43, 44, 45, 46, 47, 50, 52, 53, 54, 57, 58, 59, 62, 65, 67, 73, 75, 77, 79, 82, 83, 86, 94, 97, 98, 101, 102, 103, 106, 107, 108, 113, 116, 117, 118, 119, 122, 124, 126, 127, 128, 134, 137, 138, 139, 146, 158, 163, 164
Offset: 1

Views

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 27 2016

Keywords

Comments

If we are ever going to understand A268236 then we need to understand this sequence first.
Based on Nathan Fox's table in A268236.

Links

Crossrefs

Cf. A268236, A268237, A268238, A268540.

Formula

a(n) = A268540(n)/4 - 1

A268540 Numbers whose Fouriest transform (see A268236) is 44.

Original entry on oeis.org

24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 68, 72, 76, 80, 84, 88, 92, 96, 108, 112, 116, 128, 132, 140, 152, 156, 176, 180, 184, 188, 192, 204, 212, 216, 220, 232, 236, 240, 252, 264, 272, 296, 304, 312, 320, 332, 336, 348, 380, 392, 396, 408, 412, 416, 428, 432, 436, 456, 468, 472, 476, 480, 492, 500, 508, 512, 516
Offset: 1

Views

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 27 2016

Keywords

Comments

If we are ever going to understand A268236 then we need to understand this sequence first.
Based on Nathan Fox's extended table in A268236.
Equivalently, numbers 4k (k>5) whose representations in bases 5 through k-2 each contain at most one 4.
Equivalently, numbers 4k (k>5) whose representations in integer bases less than sqrt(4k) each contain at most one 4.
Is this sequence infinite?

Links

Crossrefs

Cf. A268236, A268237, A268238, A268541.

A268237 From the Fouriest transform of n: write n in that base b >= 4 which maximizes the number of 4's; in case of a tie pick the smallest b; sequence gives the base b.

Original entry on oeis.org

4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 6, 7, 8, 9, 5, 11, 6, 13, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 7, 7, 7, 7, 5, 8, 8, 8, 8, 5, 9, 9, 9, 9, 10, 5, 5, 5, 11, 5, 11, 11, 12, 7, 5, 12, 13, 12, 6, 5, 14, 6, 6, 6, 6, 6, 14, 7, 16, 5, 5, 5, 17, 5, 5, 16, 18, 7, 7, 5, 19, 7, 6, 7, 20, 9, 18, 18, 21, 5, 19, 19, 22, 19, 5, 5, 23, 5, 5, 5, 6
Offset: 0

Views

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 06 2016

Keywords

Comments

If no base b gives any 4's then we take b=4.
a(n) > 4 for n >= 9 since 14 is n written in base n-4. - Chai Wah Wu, Feb 06 2016

Links

Crossrefs

Cf. A268236 (Fouriest transform of n), A268238 (number of 4's).

A268238 From the Fouriest transform of n: write n in that base b >= 4 which maximizes the number of 4's; in case of a tie pick the smallest b; sequence gives the number of 4's.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2
Offset: 0

Views

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 06 2016

Keywords

Comments

If no base b gives any 4's then we take b=4.
The first occurrence of any value m in this sequence is at position 5^m-1.
a(n) > 0 for n >= 9 since 14 is n written in base n-4. - Chai Wah Wu, Feb 06 2016

Links

Crossrefs

Cf. A268236 (Fouriest transform of n), A268237 (the base b).

A268236 Fouriest transform of n: write n in that base b >= 4 which maximizes the number of 4's; in case of a tie pick the smallest b; sequence gives n in base b.

Original entry on oeis.org

0, 1, 2, 3, 4, 11, 12, 13, 20, 14, 14, 14, 14, 14, 24, 14, 24, 14, 24, 34, 40, 41, 42, 43, 44, 41, 42, 43, 44, 104, 42, 43, 44, 45, 114, 43, 44, 45, 46, 124, 44, 45, 46, 47, 44, 140, 141, 142, 44, 144, 46, 47, 44, 104, 204, 47, 44, 49, 134, 214, 44, 141, 142, 143, 144, 145
Offset: 0

Views

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 06 2016

Keywords

Comments

If no base b gives any 4's then we take b=4.
For n>65 "digits" greater than 9 appear in a(n) - see the first link. This explains why this sequence has no b-file: the OEIS restriction to decimal digits means that a(66) cannot be written as a single base-10 number (it would be "4,10").
The Fouriest transform pun suggests (by analogy with shaky, shakier, shakiest) investigating the Foury, Fourier, and Fouriest numbers. Three obvious candidates for the Foury numbers are A011534, A019764, and A268544, which are all "Foury" in different ways.
With respect to a fixed base b, we could say that n is Fourier than m (in base b) if the fraction [or number?] of 4's in the representation of n (base b) is greater than the analogous quantity for m. But it is not clear which definition is to be preferred. In base 10, which is Fourier, 440 or 439454?
This sequence and its companions were created during a dinner following the Experimental Mathematics Seminar at Rutgers University on Feb 04 2016.

Examples

			For n=24, the base-5 representation of 24 is 44. So the Fouriest transform of 24 is a(24) = 44, which uses base b = A268237(24) = 5 and contains A268238(24) = 2 4's.
The Fouriest transform of n=66 is 4,10 in base b=14 (note the non-decimal digit) and contains a single 4.

Links

Crossrefs

Cf. A268237 (the base b), A268238 (number of 4's).
See A268540 and A268541 for the "44" entries.
See also the "Foury" numbers A011534, A019764, and A268544.
A268360 and A349031 are other Foury sequences.

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

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