A010877 -id:A010877 - cp's OEIS frontend

A010886 Period 7: repeat [1, 2, 3, 4, 5, 6, 7].

1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4

Offset: 0

N. J. A. Sloane

Partial sums are given by A130485(n)+n+1. - Hieronymus Fischer, Jun 08 2007

Decimal expansion of 1234567/9999999 = 0.123456712345671234567... - Eric Desbiaux, Nov 03 2008

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

Cf. A002264, A002265, A002266, A004526, A010872, A010873, A010874, A010875, A010876, A010877, A130485.

Cf. A177160 (decimal expansion of (4502+sqrt(29964677))/6961).

&cat [[1, 2, 3, 4, 5, 6, 7]^^20]; // Wesley Ivan Hurt, Jul 18 2016

seq(op([1, 2, 3, 4, 5, 6, 7]), n=0..20); # Wesley Ivan Hurt, Jul 18 2016

PadRight[{}, 100, {1, 2, 3, 4, 5, 6, 7}] (* Wesley Ivan Hurt, Jul 18 2016 *)

a(n)=n%7+1 \\ Charles R Greathouse IV, Jul 13 2016

a(n) = 1 + (n mod 7). - Paolo P. Lava, Nov 21 2006
a(n) = A010876(n) + 1. G.f.: (Sum_{k=0..6} (k+1)*x^k)/(1-x^7). Also (7*x^8-8*x^7+1)/((1-x^7)*(1-x)^2). - Hieronymus Fischer, Jun 08 2007
From Wesley Ivan Hurt, Jul 18 2016: (Start)
a(n) = a(n-7) for n>6.
a(n) = 1 - 6*floor(n/7) + Sum_{k=1..6} floor((n + k)/7). (End)

A109753 n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.

Original entry on oeis.org

0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0

Offset: 0

Bruce Corrigan (scentman(AT)myfamily.com), Aug 11 2005

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

Cf. n mod 8 = A010877; n^2 mod 8 = A070432.

a(n)=n^3%8 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,3,8 ) for n in range(0, 105)] # - Zerinvary Lajos, Oct 29 2009

G.f. = (x+3x^3+5x^5+7x^7)/(1-x^8)

A165242 The larger member of the n-th twin prime pair, modulo 8.

Original entry on oeis.org

5, 7, 5, 3, 7, 3, 5, 1, 7, 5, 3, 7, 5, 1, 7, 5, 1, 7, 3, 1, 5, 5, 1, 7, 3, 3, 1, 3, 3, 5, 3, 7, 5, 3, 3, 5, 1, 3, 7, 5, 1, 7, 7, 3, 7, 1, 5, 5, 3, 1, 1, 5, 5, 3, 3, 5, 1, 7, 5, 7, 7, 5, 3, 1, 1, 3, 7, 7, 5, 7, 5, 7, 7, 1, 3, 1, 1, 3, 7, 3, 3, 1, 1, 1, 5, 3, 5, 3, 1, 5, 7, 7, 5, 1, 5, 7, 7, 1, 1, 7, 5, 7, 3, 3, 5

Offset: 1

Jonathan Vos Post, Sep 09 2009

Related to the rank of some elliptic curves by the conjecture on page 2 of [Hatley]:
Let E_p be the elliptic curve defined by y^2 = x(x-p)(x-2) where p and p-2 are twin primes.
Then Rank(E_p) = 0 if p == 7 (mod 8), 1 if p == 3,5 (mod 8), 2 if p == 1 (mod 8).

Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

Jeffrey Hatley, On the Rank of the Elliptic Curve y^2=x(x-p)(x-2), arXiv:0909.1614 [math.NT], 2009.

Cf. A000040, A001359, A010877.

A006512 := proc(n) if n = 1 then 5; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a-2) then RETURN(a) ; fi; od: fi; end:
A165242 := proc(n) A006512(n) mod 8 ; end: seq(A165242(n),n=1..120) ; # R. J. Mathar, Sep 16 2009

Mod[#,8]&/@(Select[Partition[Prime[Range[800]],2,1],#[[2]]-#[[1]]==2&][[All,2]]) (* Harvey P. Dale, Sep 26 2016 *)

a(n) = A010877(A006512(n)).

Redefined for the larger member of twin primes by R. J. Mathar, Sep 16 2009

A277546 a(n) = n/8^m mod 8, where 8^m is the greatest power of 8 that divides n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 2, 1, 2, 3, 4, 5, 6, 7, 3, 1, 2, 3, 4, 5, 6, 7, 4, 1, 2, 3, 4, 5, 6, 7, 5, 1, 2, 3, 4, 5, 6, 7, 6, 1, 2, 3, 4, 5, 6, 7, 7, 1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 2, 1, 2, 3, 4, 5, 6

Offset: 1

Clark Kimberling, Oct 19 2016

a(n) is the rightmost nonzero digit in the base 8 expansion of n.

			a(11) = (11/8 mod 8) = 3.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A010877.

Table[Mod[n/8^IntegerExponent[n, 8], 8], {n, 1, 160}]
m8[n_]:=Module[{idn=IntegerDigits[n,8]},While[idn[[-1]]==0,idn = Most[ idn]];idn[[-1]]]; Array[m8,90] (* Harvey P. Dale, Apr 02 2017 *)

a(n) = n/8^valuation(n, 8) % 8; \\ Michel Marcus, Oct 20 2016

A290108 a(n) = A268819(n) mod 8.

Original entry on oeis.org

0, 1, 3, 0, 6, 2, 2, 1, 4, 7, 6, 3, 1, 3, 1, 0, 0, 5, 0, 6, 0, 7, 3, 2, 0, 0, 7, 2, 6, 0, 2, 1, 0, 1, 0, 4, 4, 1, 6, 7, 3, 1, 3, 6, 6, 2, 3, 3, 1, 1, 3, 1, 4, 6, 5, 3, 6, 7, 3, 1, 3, 3, 3, 0, 3, 1, 2, 0, 4, 1, 1, 5, 6, 5, 7, 0, 0, 7, 4, 6, 0, 2, 7, 0, 6, 2, 1, 7, 3, 7, 2, 3, 5, 2, 2, 2, 1, 0, 2, 0, 3, 2, 4, 0, 3, 5, 0, 7, 4, 4, 6, 2, 2, 7, 0, 6, 1, 2, 2, 0

Offset: 1

Antti Karttunen, Sep 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65536

Cf. A010877, A165471, A268728, A268819, A269157.

(define (A290108 n) (modulo (A268819 n) 8))
;; For the rest of code, follow A268819 and A268728.

a(n) = A010877(A268819(n)) = A268819(n) mod 8.

A126048 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 8.

Original entry on oeis.org

2, 3, 5, 7, 5, 1, 3, 7, 5, 1, 3, 7, 1, 7, 7, 3, 1, 1, 5, 7, 1, 5, 5, 1, 5, 1, 1, 3, 7, 1, 3, 7, 1, 3, 5, 5, 1, 1, 5, 3, 7, 7, 1, 1, 3, 1, 1, 1

Offset: 1

Artur Jasinski, Dec 17 2006

Cf. A000043, A010877, A126043-A126059.

Mod[MersennePrimeExponent[Range[47]],8] (* Harvey P. Dale, Apr 18 2019 *)

a(n) = A010877(A000043(n)). - Ivan Panchenko, Apr 07 2018

a(45)-a(46) from Ivan Panchenko, Apr 07 2018
a(47) from Ivan Panchenko, Apr 09 2018
a(48) from Amiram Eldar, Oct 14 2024

cp's OEIS Frontend

A010886 Period 7: repeat [1, 2, 3, 4, 5, 6, 7].

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A109753 n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.

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A165242 The larger member of the n-th twin prime pair, modulo 8.

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A277546 a(n) = n/8^m mod 8, where 8^m is the greatest power of 8 that divides n.

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A290108 a(n) = A268819(n) mod 8.

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A126048 Exponents p of the Mersenne primes 2^p - 1 (see A000043) read mod 8.

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Formula

Extensions