cp's OEIS Frontend

A226233 Ten copies of each positive integer.

%I A226233 #39 Jun 13 2025 10:44:57
%S A226233 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 A226233 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 A226233 7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,10
%N A226233 Ten copies of each positive integer.
%C A226233 Class of well and totally ordered sequences of (p-1)-tuples of natural numbers for p = 11.
%C A226233 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.
%C A226233 a(n) = A132272(n-1) for n<=200, but the two sequences start to differ then. - _R. J. Mathar_, Jun 13 2025
%H A226233 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 A226233 <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 A226233 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.
%F A226233 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
%p A226233 A226233 := proc(n)
%p A226233     option remember ;
%p A226233     if n <= 10 then
%p A226233         1;
%p A226233     elif n <=20 then
%p A226233         2;
%p A226233     else
%p A226233         procname(n-1)+procname(n-10)-procname(n-11) ;
%p A226233     end if;
%p A226233 end proc:
%p A226233 seq(A226233(n),n=1..120) ; # _R. J. Mathar_, Jun 13 2025
%t A226233 p=11; k = (p - 1); alpha = (k + n - 1 - (Mod[(n - 1), k]))/k; Table[alpha, {n, 100}]
%t A226233 Table[PadRight[{},10,n],{n,10}]//Flatten (* _Harvey P. Dale_, May 24 2021 *)
%o A226233 (PARI) a(n)=(n+9)\10 \\ _Charles R Greathouse IV_, Jun 05 2013
%Y A226233 Cf. A000027, A004526, A002265.
%Y A226233 Cf. A059995 (10 copies of nonnegative integers).
%K A226233 nonn,easy
%O A226233 1,11
%A A226233 _Sam Vaseghi_, Jun 01 2013