A061829 Multiples of 5 having only odd digits.

5, 15, 35, 55, 75, 95, 115, 135, 155, 175, 195, 315, 335, 355, 375, 395, 515, 535, 555, 575, 595, 715, 735, 755, 775, 795, 915, 935, 955, 975, 995, 1115, 1135, 1155, 1175, 1195, 1315, 1335, 1355, 1375, 1395, 1515, 1535, 1555, 1575, 1595, 1715, 1735, 1755

Offset: 1

Author

Amarnath Murthy, May 29 2001

Keywords

• nonn
• base
• easy

Examples

			135 = 5*27 is a term having all odd digits.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A014261.

Programs

Maple

L[1]:= [5]:
for n from 2 to 4 do
  L[n]:= [seq(op(map(`+`,L[n-1],i*10^(n-1))),i=1..9,2)]
od:
map(op, [seq(L[i],i=1..4)]); # Robert Israel, Jun 10 2018

Mathematica

Select[5 Range[370],Select[IntegerDigits[#],EvenQ]=={}&]  (* Harvey P. Dale, Feb 07 2011 *)

PARI

is(n)=n%10==5 && #setintersect(Set(digits(n)),[0,2,4,6,8])==0 \\ Charles R Greathouse IV, Feb 15 2017

Formula

From Robert Israel, Jun 10 2018: (Start)

For n > 1, a(n) = 10*A014261(n-1) + 5.

a(5*n) = 25 + 10*a(n).

a(5*n+1) = 45 + 10*a(n).

a(5*n+2) = -35 + 10*a(n+1).

a(5*n+3) = -15 + 10*a(n+1).

a(5*n+4) = 5 + 10*a(n+1).

G.f. g(x) satisfies g(x) = -25 - 40*x + 5*(5+9*x-7*x^2-3*x^3+x^4)/(1-x^5) + 10*(1-x^5)*g(x^5)/(x^3*(1-x)).

(End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 30 2001