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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences.

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)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A014261.

Sequence in context: A051807 A034052 A233348 * A063382 A069983 A005894

Adjacent sequences: A061826 A061827 A061828 * A061830 A061831 A061832

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 29 2001

Extensions

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

Status

approved