A122098 Smallest number, different from 1, which when multiplied by "n" produces a number with "n" as its rightmost digits.

11, 6, 11, 6, 3, 6, 11, 6, 11, 11, 101, 26, 101, 51, 21, 26, 101, 51, 101, 6, 101, 51, 101, 26, 5, 51, 101, 26, 101, 11, 101, 26, 101, 51, 21, 26, 101, 51, 101, 6, 101, 51, 101, 26, 21, 51, 101, 26, 101, 3, 101, 26, 101, 51, 21, 26, 101, 51, 101, 6, 101, 51, 101, 26, 21

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 18 2006

Keywords

• nonn
• base

Comments

All prime numbers p > 5 must be multiplied by 1+10^k, where k is the number of digits of p. The result is p U p. - Paolo P. Lava, Apr 11 2008

Examples

			a(8) = 6 because 8*6 = 48 and 6 is the minimum number that multiplied by 8 gives a number ending in 8.
a(12) = 26 because 12*26 = 312 and 26 is the minimum number that multiplied by 12 gives a number ending in 12.
		

References

• Giorgio Balzarotti and Paolo P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 100.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A080501.

Programs

Maple

P:=proc(n) local a,b,i,j; print(11); for i from 2 by 1 to n do b:=trunc(evalf(log10(i)))+1; for j from 2 by 1 to n do a:=i*j; if i=a-trunc(a/10^b)*10^b then print(j); break; fi; od; od; end: P(101); # Paolo P. Lava, Apr 11 2008

Mathematica

snrd[n_]:=Module[{k=2},While[Mod[k*n,10^IntegerLength[n]]!=n,k++];k]; Array[ snrd,70] (* Harvey P. Dale, Apr 08 2019 *)

Python

def a(n):
    kn, s = 2*n, str(n)
    while not str(kn).endswith(s): kn += n
    return kn//n
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Nov 06 2021