A096022 Numbers that are congruent to {15, 27, 39, 51} mod 60.

15, 27, 39, 51, 75, 87, 99, 111, 135, 147, 159, 171, 195, 207, 219, 231, 255, 267, 279, 291, 315, 327, 339, 351, 375, 387, 399, 411, 435, 447, 459, 471, 495, 507, 519, 531, 555, 567, 579, 591, 615, 627, 639, 651, 675, 687, 699, 711, 735, 747, 759, 771, 795

Offset

1,1

Comments

Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 2 and (n+3) mod 5 <> 1.

This is one of a family of sequences which are defined (or could be defined) according to the same scheme: Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to k-1 and (n+k) mod (2+k) <> 1. We have A007310 for k = 1, A017629 for k = 2, this one (A096022) for k = 3, A096023 for k = 5, A096024 for k = 6, A096025 for k = 7, A096026 for k = 9, A096027 for k = 11. Remarkably these sequences are empty for k = 4, 8, 10, ... (i.e., if k+1 is a term of A080765).

Numbers n such that n mod 12 = 3 and n mod 60 <> 3.

Subsequence of A017557: 12n+3.

Links

Table of n, a(n) for n=1..53.

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

Formula

G.f.: 3*x*(5+4*x+4*x^2+4*x^3+3*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 04 2016: (Start)

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

a(n) = 3*(10*n-3-i^(2*n)-(1-i)*i^(-n)-(1+i)*i^n)/2 where i=sqrt(-1). (End)

E.g.f.: 3*(3 + sin(x) - cos(x) + (5*x - 1)*sinh(x) - (2 - 5*x)*cosh(x)). - Ilya Gutkovskiy, Jun 05 2016

Example

51 mod 2 = 52 mod 3 = 53 mod 4 = 1 and 54 mod 5 = 4, hence 51 is in the sequence; 3 mod 2 = 4 mod 3 = 5 mod 4 = 6 mod 5 = 1, hence 3 is not in the sequence.

Maple

A096022:=n->3*(10*n-3-I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/2: seq(A096022(n), n=1..80); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Table[3*(10n-3-I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/2, {n, 80}] (* Wesley Ivan Hurt, Jun 04 2016 *)

Prog

(PARI) {k=3; m=800; for(n=1, m, j=0; b=1; while(b&&j<k, if((n+j)%(2+j)==1, j++, b=0)); if(b&&(n+k)%(2+k)!=1, print1(n, ", ")))}
(Magma) [ n : n in [1..1500] | n mod 60 in [15, 27, 39, 51] ] // Vincenzo Librandi, Mar 24 2011

Crossrefs

Cf. A007310, A017557, A017629, A080765, A096023, A096024, A096025, A096026, A096027.

Sequence in context: A053177 A349175 A145195 * A097222 A004069 A110978

Adjacent sequences: A096019 A096020 A096021 * A096023 A096024 A096025

Keyword

nonn,easy

Author

Klaus Brockhaus, Jun 15 2004

Extensions

New definition from Ralf Stephan, Dec 01 2004

Status

approved