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A086360 The n-th primorial number reduced modulo 9.

%I A086360 #26 Nov 14 2024 14:56:12
%S A086360 1,2,6,3,3,6,6,3,3,6,3,3,3,6,6,3,6,3,3,3,6,6,6,3,6,6,3,3,6,6,3,3,6,3,
%T A086360 3,6,6,6,6,3,6,3,3,6,6,3,3,3,3,6,6,3,6,6,3,6,3,6,6,6,3,3,6,6,3,3,6,6,
%U A086360 6,3,3,6,3,3,3,3,6,3,3,6,6,3,3,6,6,6,3,6
%N A086360 The n-th primorial number reduced modulo 9.
%C A086360 a(n) is the fixed point reached by decimal-digit-sum-function (A007953), when starting the iteration from the value of the n-th primorial, A002110(n). - The (edited) original definition of the sequence, which is equal to a simple definition a(n) = A002110(n) mod 9, because taking the decimal digit sum preserves congruence modulo 9. - _Antti Karttunen_, Nov 14 2024
%C A086360 Only a(0)=1 and a(1)=2; each subsequent term is either a 3 or a 6.
%H A086360 Antti Karttunen, <a href="/A086360/b086360.txt">Table of n, a(n) for n = 0..19683</a> (terms 1..10000 from Nathaniel Johnston)
%H A086360 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A086360 a(n) = A010878(A002110(n)) = A002110(n) mod 9.
%F A086360 a(n) = A010888(A002110(n)).
%e A086360 For n=7, 7th primorial = 510510, list of iterated digit sums is {510510,12,3}, thus a(7)=3.
%p A086360 A086360 := proc(n) option remember: if(n=1)then return 2:fi: return ithprime(n)*procname(n-1) mod 9: end: seq(A086360(n), n=1..100); # _Nathaniel Johnston_, May 04 2011
%t A086360 sud[x_] := Apply[Plus, DeleteCases[IntegerDigits[x], 0]] q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] Table[FixedPoint[sud, q[w]], {w, 1, 128}]
%o A086360 (PARI)
%o A086360 up_to = 19683;
%o A086360 A086360list(up_to_n) = { my(m=9, v=vector(1+up_to_n), pr=1); v[1] = 1; for(n=1, up_to_n, pr = (pr*prime(n))%m; v[1+n] = pr); (v); };
%o A086360 v086360 = A086360list(up_to);
%o A086360 A086360(n) = v086360[1+n]; \\ _Antti Karttunen_, Nov 14 2024
%Y A086360 Cf. A002110, A007953, A010878, A010888, A029898, A038194, A086353-A086361.
%Y A086360 Cf. also A377876, A377877.
%K A086360 easy,nonn
%O A086360 0,2
%A A086360 _Labos Elemer_, Jul 21 2003
%E A086360 Term a(0)=1 prepended, old definition moved to comments and replaced with one of the formulas, keyword:base removed because not really base-dependent - _Antti Karttunen_, Nov 14 2024