A123872 Start with the seed a(0)=2. The minimum number, different from 1, that multiplied by 2 (seed) produces a number with 2 as its rightmost digit is a(1)=6. Then 6*2=12. Again, the minimum number that multiplied by 12 produces 12 as its rightmost digits is a(2)=26 (12*26=312). And so on.

2, 6, 26, 126, 6251, 62500001, 6250000000000001, 6250000000000000000000000000001, 62500000000000000000000000000000000000000000000000000000000001

Offset

0,1

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 99.

Links

Table of n, a(n) for n=0..8.

Example

a(0)=2;
a(1)=6 because 2*6 = 12;
a(2)=26 because 12*26 = 312;
a(3)=126 because 312*126 = 39312;
a(4)=6251 because 39312*6251 = 245739312;
a(5)=62500001 because 245739312*62500001 = 15358707245739312.

Maple

P:=proc(q, h) local a, b, k, n; a:=h; b:=ilog10(a)+1; print(h);
for k from 1 to 10 do for n from 2 to q do
if ((a*n) mod 10^b)=a then print(n); a:=a*n; b:=ilog10(a)+1;
break; fi; od; od; end: P(10^9, 2);

Prog

(Python)
import math
p, n = 2, 0
while n<10:
    ndigits, oldp = len(str(p)), p
    p += math.lcm(p, 10**ndigits)
    print("a(%d) = %d"%(n:=n+1, p//oldp))
# Bert Dobbelaere, Aug 08 2023

Crossrefs

Cf. A123873, A123874, A123875.

Sequence in context: A034474 A306041 A345870 * A230071 A030937 A030827

Adjacent sequences: A123869 A123870 A123871 * A123873 A123874 A123875

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 16 2006

Extensions

More terms from Bert Dobbelaere, Aug 08 2023

Status

approved