A086360 The n-th primorial number reduced modulo 9.

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, 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, 6, 3, 3, 6, 3, 3, 3, 3, 6, 3, 3, 6, 6, 3, 3, 6, 6, 6, 3, 6

Offset: 0

Author

Labos Elemer, Jul 21 2003

Keywords

• easy
• nonn

Comments

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

Only a(0)=1 and a(1)=2; each subsequent term is either a 3 or a 6.

Examples

			For n=7, 7th primorial = 510510, list of iterated digit sums is {510510,12,3}, thus a(7)=3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683 (terms 1..10000 from Nathaniel Johnston)
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A007953, A010878, A010888, A029898, A038194, A086353-A086361.

Cf. also A377876, A377877.

Programs

Maple

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

Mathematica

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}]

PARI

up_to = 19683;
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); };
v086360 = A086360list(up_to);
A086360(n) = v086360[1+n]; \\ Antti Karttunen, Nov 14 2024

Formula

a(n) = A010878(A002110(n)) = A002110(n) mod 9.

a(n) = A010888(A002110(n)).

Extensions

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