A256668 a(n) = 3*B*C*(n mod A) + 5*A*C*(n mod B) + 2*A*B*(n mod C) with A=7, B=11, C=17.

1310, 2620, 3930, 5240, 6550, 7860, 5243, 6553, 7863, 9173, 3938, 5248, 6558, 3941, 5251, 6561, 5253, 6563, 7873, 9183, 6566, 1331, 2641, 3951, 5261, 6571, 7881, 5264, 6574, 7884, 9194, 10504, 5269, 3961, 1344, 2654, 3964, 5274, 6584, 7894

Offset: 1

Author

Aaron Kastel, Apr 07 2015

Keywords

• nonn
• easy

Comments

After 0 it cycles again from 1310 (a(1309)=0 so there are 1309 (A*B*C) terms).

This is another variation on A256496, where a(n) = B*C*(n mod A) + A*C*(n mod B) + A*B*(n mod C), modified to take the values A=7, B=11, C=17 and still maintain the equivalence a(n) mod ABC = n mod ABC.

Here some modification is required (to maintain that equivalence) so that 'BC' + 'AC' + 'AB' = ABC + 1 where 'BC', 'AC' and 'AB' are the coefficients. Therefore, a(n) = 3B*C*(n mod A) + 5A*C*(n mod B) + 2A*B*(n mod C) so that 3*11*17 + 5*7*17 + 2*7*11 =7*11*17 + 1 = 561 + 595 + 154 = 1310.

This is an example with 3 modifications.

a(n) = n for n = 154, 308, 462, 561, 595, 616, 715, 749, 770, 869, 903, 924, 1023, 1057, 1078, 1122, 1156, 1177, 1190, 1211, 1232, 1276.

Links

• Aaron Kastel, Table of n, a(n) for n = 1..1309
• Index entries for linear recurrences with constant coefficients, signature (-2, -3, -4, -5, -6, -7, -7, -7, -7, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1).

Crossrefs

Cf. A255818 for an example with 1 modification and A256643 for 2 modifications.

Programs

Magma

A:=7; B:=11; C:=17; [3*B*C*(n mod A)+5*A*C*(n mod B)+2*A*B*(n mod C): n in [1..60]]; // Bruno Berselli, Apr 14 2015

Mathematica

Table[561*Mod[n,7]+595*Mod[n,11]+154*Mod[n,17],{n,40}] (* or *) LinearRecurrence[{-2,-3,-4,-5,-6,-7,-7,-7,-7,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,7,7,7,7,6,5,4,3,2,1},{1310,2620,3930,5240,6550,7860,5243,6553,7863,9173,3938,5248,6558,3941,5251,6561,5253,6563,7873,9183,6566,1331,2641,3951,5261,6571,7881,5264,6574,7884,9194,10504,5269},40]  (* Harvey P. Dale, May 03 2023 *)

PARI

my(A=7, B=11, C=17, nn = A*B*C); vector(nn, n, 3*B*C*(n % A) + 5*A*C*(n % B) + 2*A*B*(n % C)) \\ Michel Marcus, Apr 14 2015

Formula

G.f.: -x*(11780*x^31 +34030*x^30 +65440*x^29 +104700*x^28 +150500*x^27 +201530*x^26 +256480*x^25 +306187*x^24 +350651*x^23 +389872*x^22 +423850*x^21 +447350*x^20 +461682*x^19 +468156*x^18 +468082*x^17 +462770*x^16 +453530*x^15 +432510*x^14 +403638*x^13 +368224*x^12 +327578*x^11 +283010*x^10 +235830*x^9 +187348*x^8 +144109*x^7 +106113*x^6 +73360*x^5 +45850*x^4 +26200*x^3 +13100*x^2 +5240*x +1310) / ((x -1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)*(x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x +1)*(x^16 +x^15 +x^14 +x^13 +x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - Colin Barker, Apr 14 2015