A088002 -id:A088002 - cp's OEIS frontend

A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1

Offset: 0

N. J. A. Sloane

Michael Gilleland, Some Self-Similar Integer Sequences
R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A011662.

Cf. A011747..A011751 for similar sequences and A011655 - A011745 for other binary m-sequences.

series((1+x^2)/(1+x^2+x^5),x,100) mod 2;

Mod[CoefficientList[Series[(1+x^2)/(1+x^2+x^5),{x,0,80}],x],2] (* Harvey P. Dale, Jul 19 2023 *)

A011746_vec=Vec((1+x^2)/(1+x^2+x^5)+O(x^31))%2 \\ For illustrative purpose.
A011746(n)=bittest(377253537,n%31) \\ M. F. Hasler, Feb 17 2018

a(n) = A088002(n) mod 2. - R. J. Mathar, May 26 2008
G.f.: (1+x^5+x^7+x^9+x^10+x^11+x^13+x^14+x^18+x^19+x^20+x^21+x^22+x^25+x^26+x^28)/(1-x^31). - Robert Israel, May 06 2018
a(n) = A011662(n-1). - R. J. Mathar, Jan 12 2024

A088001 a(n) is the sum of non-palindromic divisors of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 12, 13, 14, 15, 16, 17, 18, 19, 30, 21, 0, 23, 36, 25, 39, 27, 42, 29, 55, 31, 48, 0, 51, 35, 66, 37, 57, 52, 70, 41, 77, 43, 0, 60, 69, 47, 100, 49, 85, 68, 91, 53, 99, 0, 98, 76, 87, 59, 147, 61, 93, 84, 112, 78, 0, 67, 119, 92, 129, 71, 162, 73

Offset: 1

Labos Elemer, Oct 14 2003

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A087999, A088000, A088002.

A088001 := proc(n)
        numtheory[sigma](n)-A088000(n) ;
end proc; # R. J. Mathar, Jul 28 2016

Table[Plus @@ Select[Divisors[k], Reverse[x = IntegerDigits[#]] != x &], {k, 73}] (* Jayanta Basu, Aug 12 2013 *)
Table[Total[Select[Divisors[n],!PalindromeQ[#]&]],{n,80}] (* Harvey P. Dale, May 15 2025 *)

def ispal(n):
    return n==int(str(n)[::-1])
def A088001(n):
    s=0
    for i in range(1, n+1):
        if n%i==0 and not ispal(i):
             s+=i
    return s # Indranil Ghosh, Feb 10 2017

a(n)=0 iff all divisors are palindromic. See A062687.

a(n)+A088000(n) = A000203(n). - R. J. Mathar, Sep 09 2015

A011662 A binary m-sequence: expansion of reciprocal of x^5 + x^2 + 1.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1

Offset: 0

N. J. A. Sloane

The auxiliary sequence with o.g.f. x^4/(1 + x^2 + x^5) can be obtained by deleting the first term in A088002 and flipping all signs. - R. J. Mathar, May 26 2008

Period 31: repeat 0,0,0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,1,1,0,1,0,0,1. - Ralf Stephan, Aug 05 2013

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Join[Table[0, 4], Mod[CoefficientList[1/(x^5 + x^2 + 1) + O[x]^77, x], 2]] (* Jean-François Alcover, Feb 23 2018 *)

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A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.

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A088001 a(n) is the sum of non-palindromic divisors of n.

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A011662 A binary m-sequence: expansion of reciprocal of x^5 + x^2 + 1.

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