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.

A112058 Mean of A112056 and A112057.

Original entry on oeis.org

48, 72, 120, 168, 192, 288, 312, 360, 408, 432, 480, 528, 552, 648, 672, 720, 768, 792, 840, 888, 912, 960, 1008, 1032, 1128, 1152, 1200, 1248, 1272, 1320, 1368, 1392, 1488, 1512, 1560, 1608, 1632, 1680, 1728, 1752, 1800, 1848, 1872, 1968
Offset: 1

Views

Author

Antti Karttunen, Aug 27 2005

Keywords

Crossrefs

a(n) = A112056(n)+1 = A112057(n)-1 = (A112056(n)+A112057(n))/2.

Programs

  • Mathematica
    a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; 4*Select[Range[1000], a112046[2#] - a112046[2# - 1] != 0 &] (* Indranil Ghosh, May 24 2017 *)
  • Python
    from sympy import jacobi_symbol as J
def a112046(n):
    i=1
    while True:
        if J(i, 2*n + 1)!=1: return i
        else: i+=1
def a(n): return a112046(2*n) - a112046(2*n - 1)
print([4*n for n in range(1, 1001) if a(n)!=0]) # Indranil Ghosh, May 24 2017

Formula

a(n) = 4*A112054(n).

A112056 Odd numbers of the form 4n-1 for which Jacobi-first-non-one(4n-1) differs from Jacobi-first-non-one(4n+1).

Original entry on oeis.org

47, 71, 119, 167, 191, 287, 311, 359, 407, 431, 479, 527, 551, 647, 671, 719, 767, 791, 839, 887, 911, 959, 1007, 1031, 1127, 1151, 1199, 1247, 1271, 1319, 1367, 1391, 1487, 1511, 1559, 1607, 1631, 1679, 1727, 1751, 1799, 1847, 1871, 1967
Offset: 1

Views

Author

Antti Karttunen, Aug 27 2005

Keywords

Comments

Here Jacobi-first-non-one(m) (for odd numbers m) is defined as the first value of i >= 1, for which Jacobi symbol J(i,m) is not +1 (i.e. is either 0 or -1).

Crossrefs

Cf. A112054, A112057, A112058.

Programs

  • Mathematica
    a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; 4*Select[Range[1000], a112046[2#] - a112046[2# - 1] != 0 &] - 1 (* Indranil Ghosh, May 24 2017 *)
  • Python
    from sympy import jacobi_symbol as J
def a112046(n):
    i=1
    while True:
        if J(i, 2*n + 1)!=1: return i
        else: i+=1
def a(n): return a112046(2*n) - a112046(2*n - 1)
print([4*n - 1 for n in range(1, 1001) if a(n)!=0]) # Indranil Ghosh, May 24 2017

Formula

a(n) = 4*A112054(n)-1.
a(n) = A112057(n)-2 = A112058(n)-1.

A298991 Indices i in A112058 where records of 17*i - 3*A112058(i)/8 occur.

Original entry on oeis.org

2, 5, 13, 21, 24, 32, 40, 43, 51, 1470, 1478, 2701, 12032, 12040, 12048, 12051, 12059, 12067, 12070, 12078, 13301, 14524, 14683, 14691, 14699, 14702, 14710, 14718, 14721, 14729
Offset: 1

Views

Author

A.H.M. Smeets, Jan 31 2018

Keywords

Crossrefs

Cf. A112046, A112056, A112057, A112058.

Programs

  • Python
    i, n, rec = 0, 0, 0
while n < 1000:
    i = i+1
    if 17*i-3*A112058(i)//8 > rec:
        n, rec = n+1, 17*i-3*A112058(i)//8
        print(n,i)
Showing 1-3 of 3 results.

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

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