A151972 Numbers that are congruent to {0, 1, 6, 10} mod 15.

0, 1, 6, 10, 15, 16, 21, 25, 30, 31, 36, 40, 45, 46, 51, 55, 60, 61, 66, 70, 75, 76, 81, 85, 90, 91, 96, 100, 105, 106, 111, 115, 120, 121, 126, 130, 135, 136, 141, 145, 150, 151, 156, 160, 165, 166, 171, 175, 180, 181, 186, 190, 195, 196, 201, 205, 210, 211, 216, 220, 225

Offset

1,3

Comments

Also, numbers n such that n^2 - n is divisible by 15.

Also, numbers n such that n^2 - n is divisible by 30.

Links

Table of n, a(n) for n=1..61.

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

Formula

G.f.: x^2*(1+5*x+4*x^2+5*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

a(n) = (30*n-41-5*i^(2*n)+(3+3*i)*i^(-n)+(3-3*i)*i^n)/8 where i=sqrt(-1).

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

E.g.f.: (20 + (15*x - 23)*cosh(x) + 3*(sin(x) + cos(x) + (5*x - 6)*sinh(x)))/4. - Ilya Gutkovskiy, Jun 07 2016

Maple

A151972:=n->(30*n-41-5*I^(2*n)+(3+3*I)*I^(-n)+(3-3*I)*I^n)/8: seq(A151972(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0, 300], Divisible[#^2-#, 15]&]  (* Harvey P. Dale, Apr 01 2011, altered by Eric M. Schmidt, Aug 05 2012 *)

Prog

(Magma) [ n : n in [0..1000] | n mod 15 in [0, 1, 6, 10]]; // Vincenzo Librandi, Apr 02 2011, simplified by Eric M. Schmidt, Aug 05 2012
(Magma) [ n: n in [0..1000] | (n^2-n) mod (15) eq 0 ]; // Vincenzo Librandi, Apr 03 2011, altered by Eric M. Schmidt, Aug 05 2012

Crossrefs

For m^2 == m (mod n), see: n=2: A001477, n=3: A032766, n=4: A042948, n=5: A008851, n=6: A032766, n=7: A047274, n=8: A047393, n=9: A090570, n=10: A008851, n=11: A112651, n=12: A112652, n=13: A112653, n=14: A047274, n=15: A151972, n=16: A151977, n=17: A151978, n=18: A090570, n=19: A151979, n=20: A151980, n=21: A151971, n=22, A112651, n=24: A151973, n=26: A112653, n=30: A151972, n=32: A151983, n=34: A151978, n=38: A151979, n=42: A151971, n=48: A151981, n=64: A151984.

Cf. A215202.

Sequence in context: A361606 A095678 A339116 * A094564 A271354 A315240

Adjacent sequences: A151969 A151970 A151971 * A151973 A151974 A151975

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 23 2009

Extensions

This is a merge of two identical sequences, A151972 and A151975.

Status

approved