A096022 -id:A096022 - cp's OEIS frontend

A096023 Numbers congruent to {63, 123, 183, 243, 303, 363} mod 420.

63, 123, 183, 243, 303, 363, 483, 543, 603, 663, 723, 783, 903, 963, 1023, 1083, 1143, 1203, 1323, 1383, 1443, 1503, 1563, 1623, 1743, 1803, 1863, 1923, 1983, 2043, 2163, 2223, 2283, 2343, 2403, 2463, 2583, 2643, 2703, 2763, 2823, 2883, 3003, 3063, 3123

Offset: 1

Klaus Brockhaus, Jun 15 2004

Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 4 and (n+5) mod 7 <> 1.

Numbers n such that n mod 60 = 3 and n mod 420 <> 3.

			63 mod 2 = 64 mod 3 = 65 mod 4 = 66 mod 5 = 67 mod 6 = 1 and 68 mod 7 = 5, hence 63 is in the sequence.

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

Cf. A007310, A017629, A096022, A096024, A096025, A096026, A096027.

Cf. A047391 (see MAGMA code). - Bruno Berselli, Mar 25 2011

[ n : n in [1..3500] | n mod 420 in [63, 123, 183, 243, 303, 363] ] // Vincenzo Librandi, Mar 24 2011

/* Alternatively:*/ &cat[ [ 60*n+3, 60*n+63 ]: n in [1..52] | n mod 7 in [1,3,5] ]; // Bruno Berselli, Mar 25 2011

A096023:=n->420*floor(n/6)+[63, 123, 183, 243, 303, 363][(n mod 6)+1]: seq(A096023(n), n=0..80); # Wesley Ivan Hurt, Jul 22 2016

Select[Range[0, 5*10^3], MemberQ[{63, 123, 183, 243, 303, 363}, Mod[#, 420]] &] (* Wesley Ivan Hurt, Jul 22 2016 *)

{k=5;m=3150;for(n=1,m,j=0;b=1;while(b&&j

G.f.: 3*x*(21+20*x+20*x^2+20*x^3+20*x^4+20*x^5+19*x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jul 22 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7; a(n) = a(n-6) + 420 for n>6.
a(n) = (210*n - 96 - 30*cos(n*Pi/3) - 30*cos(2*n*Pi/3) - 15*cos(n*Pi) + 30*sqrt(3)*sin(n*Pi/3) + 10*sqrt(3)*sin(2*n*Pi/3))/3.
a(6k) = 420k-57, a(6k-1) = 420k-117, a(6k-2) = 420k-177, a(6k-3) = 420k-237, a(6k-4) = 420k-297, a(6k-5) = 420k-357. (End)

New definition from Ralf Stephan, Dec 01 2004

A096026 Numbers k such that (k+j) mod (2+j) = 1 for j from 0 to 8 and (k+9) mod 11 <> 1.

Original entry on oeis.org

2523, 5043, 7563, 10083, 12603, 15123, 17643, 20163, 22683, 25203, 30243, 32763, 35283, 37803, 40323, 42843, 45363, 47883, 50403, 52923, 57963, 60483, 63003, 65523, 68043, 70563, 73083, 75603, 78123, 80643, 85683, 88203, 90723, 93243

Offset: 1

Klaus Brockhaus, Jun 15 2004

Numbers k such that k mod 2520 = 3 and k mod 27720 <> 3.

			2523 mod 2 = 2524 mod 3 = 2525 mod 4 = 2526 mod 5 = 2527 mod 6 = 2528 mod 7 = 2529 mod 8 = 2530 mod 9 = 2531 mod 10 = 1 and 2532 mod 11 = 2, hence 2523 is in the sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Cf. A007310, A017629, A096022, A096023, A096024, A096025, A096027.

[n: n in [1..100000] | forall{j: j in [0..8] | IsOne((n+j) mod (2+j)) and (n+9) mod 11 ne 1}]; // Bruno Berselli, Apr 11 2013

Select[Range[94000],Union[Mod[#+Range[0,8],Range[2,10]]]=={1}&&Mod[ #+9,11]!=1&] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{2523,5043,7563,10083,12603,15123,17643,20163,22683,25203,30243},40](* Harvey P. Dale, Sep 25 2019 *)

{k=9;m=95000;for(n=1,m,j=0;b=1;while(b&&j

G.f.: 3*x*(839*x^10 +840*x^9 +840*x^8 +840*x^7 +840*x^6 +840*x^5 +840*x^4 +840*x^3 +840*x^2 +840*x +841) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Apr 11 2013

A096024 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 5 and (n+6) mod 8 <> 1.

Original entry on oeis.org

423, 1263, 2103, 2943, 3783, 4623, 5463, 6303, 7143, 7983, 8823, 9663, 10503, 11343, 12183, 13023, 13863, 14703, 15543, 16383, 17223, 18063, 18903, 19743, 20583, 21423, 22263, 23103, 23943, 24783, 25623, 26463, 27303, 28143, 28983, 29823

Offset: 1

Klaus Brockhaus, Jun 15 2004

Numbers n such that n mod 840 = 423.

			423 mod 2 = 424 mod 3 = 425 mod 4 = 426 mod 5 = 427 mod 6 = 428 mod 7 = 1 and 429 mod 8 = 5, hence 423 is in the sequence.

Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A007310, A017629, A096022, A096023, A096025, A096026, A096027.

[n: n in [1..30000] | forall{j: j in [0..5] | IsOne((n+j) mod (2+j)) and (n+6) mod 8 ne 1}]; // Bruno Berselli, Apr 11 2013

{k=6;m=30000;for(n=1,m,j=0;b=1;while(b&&j

a(n) = 2*a(n-1)-a(n-2). G.f.: 3*x*(139*x+141) / (x-1)^2. - Colin Barker, Apr 11 2013

a(n) = 840*n-417. [Bruno Berselli, Apr 11 2013]

A096025 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.

Original entry on oeis.org

843, 1683, 3363, 4203, 5883, 6723, 8403, 9243, 10923, 11763, 13443, 14283, 15963, 16803, 18483, 19323, 21003, 21843, 23523, 24363, 26043, 26883, 28563, 29403, 31083, 31923, 33603, 34443, 36123, 36963, 38643, 39483, 41163, 42003, 43683

Offset: 1

Klaus Brockhaus, Jun 15 2004

Numbers n such that n mod 840 = 3 and n mod 2520 <> 3.

			843 mod 2 = 844 mod 3 = 845 mod 4 = 846 mod 5 = 847 mod 6 = 848 mod 7 = 849 mod 8 = 1 and 850 mod 9 = 4, hence 843 is in the sequence.

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

Cf. A007310, A017629, A096022, A096023, A096024, A096026, A096027.

[n: n in [1..44000] | forall{j: j in [0..6] | IsOne((n+j) mod (2+j)) and (n+7) mod 9 ne 1}]; // Bruno Berselli, Apr 11 2013

LinearRecurrence[{1,1,-1},{843,1683,3363},40] (* Harvey P. Dale, Nov 22 2015 *)

{k=7;m=44000;for(n=1,m,j=0;b=1;while(b&&j

a(n) = -3*(209+70*(-1)^n-420*n). a(n) = a(n-1)+a(n-2)-a(n-3). G.f.: 3*x*(279*x^2+280*x+281) / ((x-1)^2*(x+1)). - Colin Barker, Apr 11 2013

A096027 Numbers k such that (k+j) mod (2+j) = 1 for j from 0 to 10 and (k+11) mod 13 <> 1.

Original entry on oeis.org

27723, 55443, 83163, 110883, 138603, 166323, 194043, 221763, 249483, 277203, 304923, 332643, 388083, 415803, 443523, 471243, 498963, 526683, 554403, 582123, 609843, 637563, 665283, 693003, 748443, 776163, 803883, 831603, 859323, 887043

Offset: 1

Klaus Brockhaus, Jun 15 2004

Numbers k such that k mod 27720 = 3 and k mod 360360 <> 3.

			27723 mod 2 = 27724 mod 3 = 27725 mod 4 = 27726 mod 5 = 27727 mod 6 = 27728 mod 7 = 27729 mod 8 = 27730 mod 9 = 27731 mod 10 = 27731 mod 11 = 27731 mod 12 = 1 and 27732 mod 13 = 3, hence 27723 is in the sequence.

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

Cf. A007310, A017629, A096022, A096023, A096024, A096025, A096026.

[n: n in [1..900000] | forall{j: j in [0..10] | IsOne((n+j) mod (2+j)) and (n+11) mod 13 ne 1}]; // Bruno Berselli, Apr 11 2013

{k=11;m=900000;for(n=1,m,j=0;b=1;while(b&&j

G.f.: 3*x*(9239*x^12 +9240*x^11 +9240*x^10 +9240*x^9 +9240*x^8 +9240*x^7 +9240*x^6 +9240*x^5 +9240*x^4 +9240*x^3 +9240*x^2 +9240*x +9241) / ((x -1)^2*(x +1)*(x^2 -x +1)*(x^2 +1)*(x^2 +x +1)*(x^4 -x^2 +1)). - Colin Barker, Apr 11 2013

cp's OEIS Frontend

A096023 Numbers congruent to {63, 123, 183, 243, 303, 363} mod 420.

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A096026 Numbers k such that (k+j) mod (2+j) = 1 for j from 0 to 8 and (k+9) mod 11 <> 1.

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A096024 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 5 and (n+6) mod 8 <> 1.

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A096025 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.

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A096027 Numbers k such that (k+j) mod (2+j) = 1 for j from 0 to 10 and (k+11) mod 13 <> 1.

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