A224478 (16^(5^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 5.

0, 25, 875, 4375, 59375, 609375, 2109375, 37109375, 287109375, 6787109375, 31787109375, 581787109375, 5081787109375, 90081787109375, 240081787109375, 8740081787109375, 93740081787109375, 243740081787109375, 2743740081787109375, 57743740081787109375

Offset: 1

Author

Eric M. Schmidt, Apr 07 2013

Keywords

• nonn
• base

Comments

a(n) is the unique nonnegative integer less than 10^n such that a(n) + 2^(n-1) + 1 is divisible by 2^n and a(n) is divisible by 5^n.

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Trimorphic Number
• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A033819. Converges to the 10-adic number A091663. The other trimorphic numbers ending in 5 are included in A007185, A216093, and A224477.

Programs

Sage

def A224478(n) : return crt(2^(n-1)-1, 0, 2^n, 5^n)

Formula

a(n) = (A016090(n) + 10^n/2 - 1) mod 10^n.