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A169600 Numbers that are congruent to {4, 25} mod 31. 1
4, 25, 35, 56, 66, 87, 97, 118, 128, 149, 159, 180, 190, 211, 221, 242, 252, 273, 283, 304, 314, 335, 345, 366, 376, 397, 407, 428, 438, 459, 469, 490, 500, 521, 531, 552, 562, 583, 593, 614, 624, 645, 655, 676, 686, 707, 717, 738, 748, 769, 779, 800, 810, 831, 841, 862, 872, 893, 903, 924, 934 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: For no n >4 in the sequence, 36*n^2+72*n+35 = (6*n+5)*(6*n+7) is of the form p*(p+2), where p and p+2 are primes.

The conjecture is evident, it can be proved as in A169599. [Bruno Berselli, Jan 07 2013]

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) = (62*n  + 11*(-1)^n - 35)/4. - Vincenzo Librandi, Jan 06 2013, modified Jul 07 2015

a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Jan 06 2013

G.f.: x*(4+21*x+6*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015

MATHEMATICA

Select[Range[934], MemberQ[{4, 25}, Mod[#, 31]]&] (* Ray Chandler, Jul 08 2015 *)

LinearRecurrence[{1, 1, -1}, {4, 25, 35}, 61] (* Ray Chandler, Jul 08 2015 *)

Rest[CoefficientList[Series[x*(4+21*x+6*x^2)/((1+x)*(x-1)^2), {x, 0, 61}], x]] (* Ray Chandler, Jul 08 2015 *)

CROSSREFS

Sequence in context: A303183 A175052 A240164 * A267765 A231176 A199772

Adjacent sequences:  A169597 A169598 A169599 * A169601 A169602 A169603

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Dec 03 2009

EXTENSIONS

Added missing leading terms. Clarified the comment. - R. J. Mathar, Jul 07 2015

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)