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A047260
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Numbers that are congruent to {0, 1, 4, 5} mod 6.
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3
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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)
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MAPLE
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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
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MATHEMATICA
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Table[(6n-5-I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
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PROG
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(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
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CROSSREFS
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Cf. A007310, A047233, A047269.
Complement: A047243.
Sequence in context: A010391 A010419 A255137 * A284790 A172999 A284371
Adjacent sequences: A047257 A047258 A047259 * A047261 A047262 A047263
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Wesley Ivan Hurt, May 21 2016
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STATUS
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approved
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