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

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

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

Formula

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

Example

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.

Prog

(PARI) {k=11; m=900000; 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..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

Crossrefs

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

Sequence in context: A023943 A210161 A358414 * A249000 A058419 A235208

Adjacent sequences: A096024 A096025 A096026 * A096028 A096029 A096030

Keyword

nonn,easy

Author

Klaus Brockhaus, Jun 15 2004

Status

approved