A224475 (2*5^(2^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 9.

4, 99, 749, 6249, 31249, 281249, 781249, 75781249, 925781249, 1425781249, 86425781249, 336425781249, 4836425781249, 69836425781249, 19836425781249, 7519836425781249, 62519836425781249, 12519836425781249, 9512519836425781249, 34512519836425781249

Offset: 1

Author

Eric M. Schmidt, Apr 07 2013

Keywords

• nonn
• base

Comments

a(n) is the unique positive integer less than 10^n such that a(n) + 2^(n-1) - 1 is divisible by 2^n and a(n) + 1 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 A091661. The other trimorphic numbers ending in 9 are included in A002283, A198971, and A224473.

Programs

Mathematica

Table[Mod[2*5^2^n+(10^n/2)-1,10^n],{n,20}] (* Harvey P. Dale, Sep 08 2024 *)

Sage

def A224475(n) : return crt(2^(n-1)+1, -1, 2^n, 5^n)

Formula

a(n) = (A224473(n) + 10^n / 2) mod 10^n.