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A156619 Numbers congruent to {7, 18} mod 25. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

Numbers of the form 25*n+7 or 25*n+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

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: A103571 A103572 A049532 * A033537 A352741 A225286

Adjacent sequences: A156616 A156617 A156618 * A156620 A156621 A156622

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 11 2009

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)