A151971 Numbers n such that n^2 - n is divisible by 21.

0, 1, 7, 15, 21, 22, 28, 36, 42, 43, 49, 57, 63, 64, 70, 78, 84, 85, 91, 99, 105, 106, 112, 120, 126, 127, 133, 141, 147, 148, 154, 162, 168, 169, 175, 183, 189, 190, 196, 204, 210, 211, 217, 225, 231, 232, 238, 246, 252, 253, 259, 267, 273, 274, 280, 288, 294, 295, 301, 309

Offset: 1

Author

N. J. A. Sloane, Aug 23 2009

Keywords

• nonn
• easy

Comments

Equivalently, numbers that are congruent to {0, 1, 7, 15} mod 21. - Bruno Berselli, Aug 06 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

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.

Programs

Magma

[n: n in [0..309] | IsZero((n^2-n) mod 21)]; // Bruno Berselli, Aug 06 2012

Maple

A151971:=n->(42*n+14*I^((n-1)*n)-3*I^(2*n)-3)/8-7: seq(A151971(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0,400], Divisible[#^2-#,21]&] (* Harvey P. Dale, Jun 04 2012 *)

Maxima

makelist((42*n+14*%i^((n-1)*n)-3*(-1)^n-3)/8-7, n, 1, 60); /* Bruno Berselli, Aug 06 2012 */

Formula

From Bruno Berselli, Aug 06 2012: (Start)

G.f.: x^2*(1+6*x+8*x^2+6*x^3)/((1+x)*(1-x)^2*(1+x^2)).

a(n) = (42*n +14*i^((n-1)*n) -3*(-1)^n -3)/8 -7, where i=sqrt(-1). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Wesley Ivan Hurt, Jun 07 2016

E.g.f.: (24 + (21*x - 31)*cosh(x) + 7*(sin(x) + cos(x) + (3*x - 4)*sinh(x)))/4. - Ilya Gutkovskiy, Jun 07 2016