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

1,11

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

Table of n, a(n) for n=1..91.

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).

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

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 *)

Prog

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

Crossrefs

Cf. A000027, A004526, A002265.

Cf. A059995 (10 copies of nonnegative integers).

Sequence in context: A111852 A342676 A133880 * A329624 A059995 A132272

Adjacent sequences: A226230 A226231 A226232 * A226234 A226235 A226236

Keyword

nonn,easy

Author

Sam Vaseghi, Jun 01 2013

Status

approved