A061808 a(n) is the smallest number with all digits odd that is divisible by 2n-1.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 315, 115, 75, 135, 319, 31, 33, 35, 37, 39, 533, 559, 135, 517, 539, 51, 53, 55, 57, 59, 793, 315, 195, 335, 759, 71, 73, 75, 77, 79, 1377, 913, 595, 957, 979, 91, 93, 95, 97, 99, 1111, 515, 315, 535, 1199, 111, 113, 115, 117, 119, 1331, 1353, 375, 1397, 1935

Offset: 1

Author

Amarnath Murthy, May 28 2001

Keywords

• base
• nonn
• look

Comments

From Yang Haoran, Dec 02 2017, edited by M. F. Hasler, Mar 05 2025: (Start)

Record value for a(n) = (2n-1) * A296009(n):

(1, 3, 5, ..., 19) * 1 = (1, 3, 5, ..., 19)

21 * 15 = 315

29 * 11 = 319

41 * 13 = 533

43 * 13 = 559

61 * 13 = 793

81 * 17 = 1377

127 * 11 = 1397

129 * 15 = 1935

149 * 13 = 1937

167 * 19 = 3173

169 * 33 = 5577

201 * 155 = 31155

299 * 105 = 31395

401 * 133 = 53333

601 * 119 = 71519

633 * 283 = 179139

(complete up to here)

...

990001 * 12121113 = 11999913991113 (the first A296009(n) > 2n-1).

(End)

All terms must be odd. - M. F. Hasler, Mar 05 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Mathematical Excalibur, Problem 300, Vol. 1 No. 3 (2008), p. 3.

Crossrefs

Cf. A061807, A014261.

Equals A296009 * (2n-1).

Programs

Magma

a:=[]; for n in [1..120 by 2] do k:=1; while not Set(Intseq(n*k)) subset {1,3,5,7,9} do k:=k+2; end while; Append(~a,k*n); end for; a; // Marius A. Burtea, Sep 20 2019

Maple

Ad[1]:= [1,3,5,7,9]:
for n from 2 to 9 do Ad[n]:= map(t -> seq(10*t+j,j=[1,3,5,7,9]), Ad[n-1]) od:
Aod:= [seq(op(Ad[i]),i=1..9)]:
f:= proc(n) local k;
   for k from 1 to nops(Aod) do
       if Aod[k] mod (2*n-1) = 0 then return(Aod[k]) fi
     od;
     NotFound
end proc:
map(f, [$1..100]); # Robert Israel, Feb 15 2017

Mathematica

Table[Block[{k = 2 n - 1}, While[Nand[AllTrue[IntegerDigits@ k, OddQ], Divisible[k, 2 n - 1]], k += 2]; k], {n, 59}] (* Michael De Vlieger, Dec 02 2017 *)

PARI

isoddd(n) = #select(x->((x%2) == 0), digits(n)) == 0;
a(n) = {my(m = 2*n-1, k = 1); while(!isoddd(k*m), k++); k*m;} \\ Michel Marcus, Sep 20 2019

PARI

apply( {A061808(n)=forstep(k=n*2-1,oo,n*4-2,vecmin(digits(k)%2)&& return(k))}, [1..99])

Python

A061808 = lambda n: next(m for m in range(2*n-1,9<<99,4*n-2) if all(int(d)&1 for d in str(m))) # M. F. Hasler, Mar 05 2025

Formula

From M. F. Hasler, Mar 05 2025: (Start)

a(n) = (2n-1)*A296009(n).

a(n) == 1 (mod 2) for all n. (End)

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 30 2001