A028898 Map n = Sum c_i 10^i to a(n) = Sum c_i 3^i.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Comments

If n is a multiple of 7, then a(n) is also a multiple of 7. See the Bhattacharyya link. - Michel Marcus, May 11 2016

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Malay Bhattacharyya, Sanghamitra Bandyopadhyay, Ujjwal Maulik, Non-primes are recursively divisible, Acta Universitatis Apulensis, No 19/2009.

Crossrefs

Cf. A008589 (multiples of 7).

Different from A081502 for n>=100.

Programs

Maple

a:= proc(n) option remember;   n mod 10 + 3*procname(floor(n/10))
end proc:
a(0):= 0:
seq(a(i),i=0..100); # Robert Israel, May 11 2016

Mathematica

a = {1}; Do[AppendTo[a, If[Mod[n, 10] == 0, 3 a[[n/10]], a[[n - 1]] + 1]], {n, 2, 76}]; {0}~Join~a (* Michael De Vlieger, May 10 2016 *)

PARI

a(n)=if(n<1,0,if(n%10,a(n-1)+1,3*a(n/10)))

PARI

a(n) = subst(Pol(digits(n)), x, 3); \\ Michel Marcus, May 10 2016

Formula

a(0)=0, a(n)=3*a(n/10) if n==0 (mod 10), a(n)=a(n-1)+1 otherwise. - Benoit Cloitre, Dec 21 2002

G.f.: G(x) = (1-x)^(-1) * Sum_{i>=0} 3^i*p(x^(10^i)) where p(t) = (t+2*t^2+3*t^3+4*t^4+5*t^5+6*t^6+7*t^7+8*t^8+9*t^9)/(1+t+t^2+t^3+t^4+t^5+t^6+t^7+t^8+t^9) satisfies (1-x)*G(x) = p(x) + 3*(1-x^10)*G(x^10). - Robert Israel, May 11 2016

Extensions

More terms from Erich Friedman

Moved Wesley Ivan Hurt's formula to A081502 where it applies. - Kevin Ryde, Dec 03 2019