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

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

1,1

Comments

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

Links

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).

Formula

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

Example

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.

Mathematica

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 *)

Prog

(PARI) {k=9; m=95000; 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..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

Crossrefs

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

Sequence in context: A264339 A045942 A308735 * A278003 A308736 A031984

Adjacent sequences: A096023 A096024 A096025 * A096027 A096028 A096029

Keyword

nonn,easy,changed

Author

Klaus Brockhaus, Jun 15 2004

Status

approved