A156619 Numbers congruent to {7, 18} mod 25.

7, 18, 32, 43, 57, 68, 82, 93, 107, 118, 132, 143, 157, 168, 182, 193, 207, 218, 232, 243, 257, 268, 282, 293, 307, 318, 332, 343, 357, 368, 382, 393, 407, 418, 432, 443, 457, 468, 482, 493, 507, 518, 532, 543, 557, 568, 582, 593, 607, 618, 632, 643, 657, 668

Offset

1,1

Comments

Also, numbers k such that k^2 + 1 == 0 (mod 25).

Numbers of the form 25*k+7 or 25*k+18. Numbers b such that 25 is a base-b Euler pseudoprime. - Karsten Meyer, Jan 05 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 2*a(n-1)-a(n-2)-3, if n is even, and a(n) = 2*a(n-1)-a(n-2)+3, if n is odd, with a(1)=7, a(2)=18.

From R. J. Mathar, Feb 19 2009: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3).

a(n) = 25*n/2-25/4-3*(-1)^n/4.

G.f.: x*(7+11*x+7*x^2)/((1+x)*(1-x)^2). (End)

E.g.f.: 7 + ((50*x - 25)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 08 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(11*Pi/50)*Pi/25. - Amiram Eldar, Feb 26 2023

Mathematica

fQ[n_] := Mod[n^2 + 1, 25] == 0; Select[ Range@ 670, fQ]
Flatten[#+{7, 18}&/@(25*Range[0, 30])] (* Harvey P. Dale, Jan 24 2013 *)
Select[Range[1, 700], MemberQ[{7, 18}, Mod[#, 25]]&] (* Vincenzo Librandi, Apr 08 2013 *)

Prog

(Magma) [n: n in [1..700] | n mod 25 in [7, 18]]; // Vincenzo Librandi, Apr 08 2013

Crossrefs

Sequence in context: A365414 A103572 A049532 * A033537 A352741 A225286

Adjacent sequences: A156616 A156617 A156618 * A156620 A156621 A156622

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 11 2009

Status

approved