A226233 Ten copies of each positive integer.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 1

Author

Sam Vaseghi, Jun 01 2013

Keywords

• nonn
• easy

Comments

Class of well and totally ordered sequences of (p-1)-tuples of natural numbers for p = 11.

Given a prime p the class of sequences a(n,p) can be constructed. The above example is for p=11. The class of well and totally ordered sequences of (prime-1)-tuples of natural numbers contains all sequences a(n) according to FORMULA for primes p. The class is crucial and will be applied to define other sequences, that will be submitted to OEIS as well a posterior.

a(n) = A132272(n-1) for n<=200, but the two sequences start to differ then. - R. J. Mathar, Jun 13 2025

Links

• S. Vaseghi (alias al-Hwarizmi), Combination of positive integers in terms of primes (sophisticated version 2)
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A000027, A004526, A002265.

Cf. A059995 (10 copies of nonnegative integers).

Programs

Maple

A226233 := proc(n)
    option remember ;
    if n <= 10 then
        1;
    elif n <=20 then
        2;
    else
        procname(n-1)+procname(n-10)-procname(n-11) ;
    end if;
end proc:
seq(A226233(n),n=1..120) ; # R. J. Mathar, Jun 13 2025

Mathematica

p=11; k = (p - 1); alpha = (k + n - 1 - (Mod[(n - 1), k]))/k; Table[alpha, {n, 100}]
Table[PadRight[{},10,n],{n,10}]//Flatten (* Harvey P. Dale, May 24 2021 *)

PARI

a(n)=(n+9)\10 \\ Charles R Greathouse IV, Jun 05 2013

Formula

a(n,p) = ((p-1) + n - (1 + ((n-1) mod (p-1))))/(p-1); p is a prime and n positive integer; for this sequence p = 11.

G.f.: x / ( (1+x)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Jun 13 2025