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

1,1

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A080501.

Sequence in context: A193813 A338920 A080501 * A347518 A115943 A122088

Adjacent sequences: A122095 A122096 A122097 * A122099 A122100 A122101

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 18 2006

Status

approved