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A122098
Smallest number, different from 1, which when multiplied by "n" produces a number with "n" as its rightmost digits.
2
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
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved