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Ten copies of each positive integer.
2

%I #36 Feb 12 2024 13:29:05

%S 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,

%T 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,

%U 7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,10

%N Ten copies of each positive integer.

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

%C 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.

%H S. Vaseghi (alias al-Hwarizmi), <a href="http://math.stackexchange.com/questions/407890/combination-of-positive-integers-in-terms-of-primes-sophisticated-version-2">Combination of positive integers in terms of primes (sophisticated version 2)</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).

%F 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.

%t p=11; k = (p - 1); alpha = (k + n - 1 - (Mod[(n - 1), k]))/k; Table[alpha, {n, 100}]

%t Table[PadRight[{},10,n],{n,10}]//Flatten (* _Harvey P. Dale_, May 24 2021 *)

%o (PARI) a(n)=(n+9)\10 \\ _Charles R Greathouse IV_, Jun 05 2013

%Y Cf. A000027, A004526, A002265.

%Y Cf. A059995 (10 copies of nonnegative integers).

%K nonn,easy

%O 1,11

%A _Sam Vaseghi_, Jun 01 2013