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A047260 Numbers that are congruent to {0, 1, 4, 5} mod 6. 3
0, 1, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 25, 28, 29, 30, 31, 34, 35, 36, 37, 40, 41, 42, 43, 46, 47, 48, 49, 52, 53, 54, 55, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 76, 77, 78, 79, 82, 83, 84, 85, 88, 89, 90, 91, 94, 95, 96, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers x which are not a solution to 3^x - 2^x == 5 mod 7. - Cino Hilliard, May 14 2003

The sequence is the interleaving of A047233 with A007310. - Guenther Schrack, Feb 13 2019

LINKS

Guenther Schrack, Table of n, a(n) for n = 1..10006

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

FORMULA

G.f.: x^2*(1+3*x+x^2+x^3) / ((1+x)*(1+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 21 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (6*n - 5 - i^(2*n) + (1-i)*i^(-n) + (1+i)*i^n)/4 where i=sqrt(-1).

a(2*n) = A007310(n), a(2*n-1) = A047233(n). (End)

From Guenther Schrack, Feb 13 2019: (Start)

a(n) = (6*n - 5 - (-1)^n + 2*(-1)^(n*(n + 1)/2))/4.

a(n) = a(n-4) + 6, a(1)=0, a(2)=1, a(3)=4, a(4)=5, for n > 4.

a(-n) = -A047269(n+2). (End)

MAPLE

A047260:=n->(6*n-5-I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/4: seq(A047260(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

MATHEMATICA

Table[(6n-5-I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)

PROG

(MAGMA) [n : n in [0..100] | n mod 6 in [0, 1, 4, 5]]; // Wesley Ivan Hurt, May 21 2016

(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(1+3*x+x^2+x^3)/((1-x)*(1-x^4)))) \\ G. C. Greubel, Feb 16 2019

(Sage) a=(x^2*(1+3*x+x^2+x^3)/((1-x)*(1-x^4))).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019

(GAP) Filtered([0..100], n->n mod 6 = 0 or n mod 6 = 1 or n mod 6 = 4 or n mod 6 = 5); # Muniru A Asiru, Feb 19 2019

CROSSREFS

Cf. A007310, A047233, A047269.

Complement: A047243.

Sequence in context: A010391 A010419 A255137 * A284790 A172999 A284371

Adjacent sequences:  A047257 A047258 A047259 * A047261 A047262 A047263

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 21 2016

STATUS

approved

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Last modified October 13 19:35 EDT 2019. Contains 327981 sequences. (Running on oeis4.)