A062886 Smallest multiple of 2n+1 with property that digits are odd and each digit is two more (mod 10) than the previous digit; or 0 if no such number exists.

1, 3, 5, 7, 9, 913, 13, 135, 357, 57, 357, 1357, 0, 135, 9135, 91357, 9135791357913, 35, 13579, 13579135791, 7913, 3579135791357913, 135, 913579135791, 79135, 357, 1357913, 7913579135, 57, 1357, 7913579135791357913579, 9135, 791357913579135791357913579135

Offset: 0

Author

Amarnath Murthy, Jun 28 2001

Keywords

• nonn
• base

Comments

The size of terms of this sequence varies wildly. For example, a(453) has 755 digits, while a(456)=913. The only numbers n for which a(n)=0 up to n=500 are those for which 2*n+1 is divisible by 25. - Nathaniel Johnston, May 19 2011

Examples

			a(7) = 135 = 3*(2*7 + 1) has increasing odd digits.
a(12) does not exist because a number in base 10 divisible by 25 ends with 00, 25, 50 or 75, so a(12)=0.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A062884, A062885.

Programs

Maple

A062886 := proc(n) local d,j,k,p,val: p:=2*n+1: if(p mod 25 = 0)then return 0: fi: for j from 1 do for d from 1 to 9 by 2 do val:=0: for k from 1 to j do val:=val+10^(j-k)*((d+2*(k-1)) mod 10): od: if(val mod p = 0)then return val: fi: od: od: end: seq(A062886(n),n=0..30); # Nathaniel Johnston, May 19 2011

Mathematica

a[n_] := Module[{d, j, k, p, val}, p = 2*n+1; If[p ~Mod~ 25 == 0, Return[0]]; For[j = 1, True, j++, For[d = 1, d <= 9, d += 2, val = 0; For[k = 1, k <= j, k++, val = val + 10^(j-k)*((d + 2*(k-1)) ~Mod~ 10)]; If[val ~Mod~ p == 0, Return[val]]]]];
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Apr 17 2025, after Nathaniel Johnston *)

Extensions

More terms from Sascha Kurz, Mar 23 2002

a(6) and example corrected by, and terms after a(15) from Nathaniel Johnston, May 19 2011