A256496 a(n) = 15(n mod 2) + 10(n mod 3) + 6(n mod 5).

31, 32, 33, 34, 35, 6, 37, 38, 39, 10, 41, 12, 43, 44, 15, 16, 47, 18, 49, 20, 21, 22, 53, 24, 25, 26, 27, 28, 59, 0, 31, 32, 33, 34, 35, 6, 37, 38, 39, 10, 41, 12, 43, 44, 15, 16, 47, 18, 49, 20, 21, 22, 53, 24, 25, 26, 27, 28, 59, 0, 31, 32, 33, 34, 35, 6

Offset

1,1

Comments

After 0 it cycles again from 31.

This is the simplest example of a(n) = b*c*(n mod a) + a*c*(n mod b) + a*b*(n mod c) with a=2, b=3, c=5.

a(n) mod abc = n mod abc.

Other values for a,b,c require modification so that bc + ac + ab = abc + 1. For example, for a=3, b=5, c=7, a(n)= 2b*c*(n mod a) + a*c*(n mod b) + a*b*(n mod c) so that 2*5*7 + 3*7 + 3*5 = 3*5*7 = 70 + 21 + 15 = 106.

This expression (with a=3, b=5, c=7) (A255818) is found in the Kol Bo (Hebrew: כלבו), a book of religious Jewish law from the 13th to 14th centuries. It is given there as a method for calculating a person's age without anyone saying it explicitly.

a(n) = n for n = 6, 10, 12, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 47, 49, 53, 59.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Aaron Hacohen from Lunil?, כלבו (in Hebrew).

Menachem Mendel Schneerson, אגרות קודש (in Hebrew).

Wikipedia, Kol Bo

Index entries for linear recurrences with constant coefficients, signature (-2,-2,-1,0,1,2,2,1).

Formula

a(n) = 15(n mod 2) + 10(n mod 3) + 6(n mod 5).

G.f.: -x*(59*x^6+146*x^5+201*x^4+195*x^3+159*x^2+94*x+31) / ((x-1)*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Apr 07 2015

a(n) = -2*a(n-1) - 2*a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) + 2*a(n-7) + a(n-8), for n>=9. - Vaclav Kotesovec, Apr 07 2015

Mathematica

Table[15 Mod[n, 2] + 10 Mod[n, 3] + 6 Mod[n, 5], {n, 60}] (* Michael De Vlieger, Mar 31 2015 *)
LinearRecurrence[{-2, -2, -1, 0, 1, 2, 2, 1}, {31, 32, 33, 34, 35, 6, 37, 38}, 70] (* or *) PadRight[ {}, 70, {31, 32, 33, 34, 35, 6, 37, 38, 39, 10, 41, 12, 43, 44, 15, 16, 47, 18, 49, 20, 21, 22, 53, 24, 25, 26, 27, 28, 59, 0}] (* Harvey P. Dale, Oct 31 2016 *)

Prog

(PARI) vector(30, n, 15*(n%2) + 10*(n%3) + 6*(n%5)) \\ Michel Marcus, Mar 31 2015

Crossrefs

Cf. A255818 for an example with 1 modification, A256643 for 2 modifications and A256668 for 3 modifications.

Sequence in context: A369409 A165852 A291523 * A133782 A022401 A042936

Adjacent sequences: A256493 A256494 A256495 * A256497 A256498 A256499

Keyword

nonn,easy

Author

Aaron Kastel, Mar 31 2015

Status

approved