Eric Ginsburg - cp's OEIS frontend

User: Eric Ginsburg

Eric Ginsburg has authored 2 sequences.

A275161 Number of sides of a polygon formed by tiling n squares in a spiral.

4, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6

Offset: 1

Eric Ginsburg, Nov 13 2016

			From _Jon E. Schoenfield_, Nov 20 2016: (Start)
The order in which tiles are added to the spiral follows the numbering in the figure below:
.
  +----+----+----+----+----+
  | 25 | 10 | 11 | 12 | 13 |
  +----+----+----+----+----+
  | 24 |  9 |  2 |  3 | 14 |
  +----+----+----+----+----+
  | 23 |  8 |  1 |  4 | 15 |
  +----+----+----+----+----+
  | 22 |  7 |  6 |  5 | 16 |
  +----+----+----+----+----+
  | 21 | 20 | 19 | 18 | 17 |
  +----+----+----+----+----+
(End)

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A002620, A240025.

Table[If[Floor[Floor[Sqrt[4*n + 1]]^2/4] == n, 4, 6], {n, 1, 100}] (* Vaclav Kotesovec, Dec 02 2021 *)

a(n)=if(sqrtint(4*n+1)^2\4==n, 4, 6) \\ Charles R Greathouse IV, Nov 20 2016

a(n) = 4 for n in A002620, 6 otherwise. - Jon E. Schoenfield, Nov 19 2016

a(n) = 6 - 2*A240025(n). [See above] - Antti Karttunen, Nov 30 2021

A277116 Number of segments used to represent the number n on a 7-segment display: variant where digits 6, 7 and 9 use 6, 3 and 5 segments, respectively.

Original entry on oeis.org

6, 2, 5, 5, 4, 5, 6, 3, 7, 5, 8, 4, 7, 7, 6, 7, 8, 5, 9, 7, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 10, 6, 9, 9, 8, 9, 10, 7, 11, 9, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 12, 8, 11, 11, 10, 11, 12, 9, 13, 11, 9, 5, 8, 8, 7, 8, 9

Offset: 0

Eric Ginsburg, Sep 30 2016

Another version of A006942. Here the digit "6" is represented with six segments (the same as in A006942) but the digit "9" is represented with five segments instead of six segments. - Omar E. Pol, Sep 30 2016
If we mark with * resp. ' the graphical representations which use one more resp. one less segment, we have the following variants:
  A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),
  ___________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*).
  Sequences A234691 and A234692 make precise which segments are lit in each digit. They are related through the Hamming weight function A000120, e.g., A010371(n) = A000120(A234691(n)) = A000120(A234692(n)). - M. F. Hasler, Jun 17 2020

			For n = 29, digit '2' uses 5 segments and digit '9' uses 5 segments. So, a(29) = 10. - _Indranil Ghosh_, Feb 02 2017
The digits are represented as follows:
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|   | . - _M. F. Hasler_, Jun 17 2020

Indranil Ghosh, Table of n, a(n) for n = 0..50000
Wikipedia, Seven-segment display.
Index entries for sequences related to calculator display

Segment variations: A006942, A010371, A063720, A074458.

Cf. A102683, A234691, A234692.

Table[Total[IntegerDigits[n] /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 6 -> 6, 7 -> 3, 8 -> 7, 9 -> 5}], {n, 0, 120}] (* Michael De Vlieger, Sep 30 2016 *)

a(n) = my(segm=[6, 2, 5, 5, 4, 5, 6, 3, 7, 5], d=digits(n), s=0); if(n==0, s=6, for(k=1, #d, s=s+segm[d[k]+1])); s \\ Felix Fröhlich, Oct 05 2016

def A277116(n):
    s=0
    for i in str(n):
        s+=[6,2,5,5,4,5,6,3,7,5][int(i)]
    return s # Indranil Ghosh, Feb 02 2017

a(n) = A006942(n) - A102683(n). - Omar E. Pol, Sep 30 2016
a(n) = A063720(n) + A102677(n) - A102679(n) (add number of digits 6)
  = A074458(n) - A102679(n) + A102681(n) (subtract number of digits 7)
  and thus A063720(n) <= a(n) <= min(A074458(n), A006942(n)) <= A010371(n). - M. F. Hasler, Jun 17 2020

Better definition and more terms from Omar E. Pol, Sep 30 2016

Edited by M. F. Hasler, Jun 17 2020

cp's OEIS Frontend

User: Eric Ginsburg

A275161 Number of sides of a polygon formed by tiling n squares in a spiral.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula