A364837 Initial digit of 2^(2^n) = A001146(n).

2, 4, 1, 2, 6, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 2, 4, 1, 2, 6, 4, 2, 4, 1, 3, 1, 1, 1, 2, 4, 1, 3, 9, 9, 8, 7, 5, 2, 8, 8, 6, 4, 1, 3, 9, 9, 9, 9, 9, 8, 7, 5, 2, 8, 7, 6, 3, 1, 2, 5, 3, 1, 1, 1, 3, 1, 1, 3, 9, 8, 7, 5, 3, 1, 1, 1, 3, 1, 2, 4, 2, 5, 2, 6, 4, 1, 2

Offset

0,1

Comments

The sequence corresponds to the initial digit of 2vvn (since 2^(2^n) = ((((2^2)^2)^...)^2) (n times)), where vv indicates weak tetration (see links).

Conjecture: this sequence obeys Benford's law.

For any n > 1, the final digit of 2^(2^n) is 6.

Links

Table of n, a(n) for n=0..87.

Pointless Large numbers stuff by Cookiefonster, 2.03 The Weak Hyper-Operators.

Formula

a(n) = floor(2^(2^n)/10^floor(log_10(2^(2^n)))), for n > 0.

a(n) = A000030(A001146(n)).

Example

a(5) = 4, since 2^(2^5) = 2^32 = 4294967296.

Mathematica

Join[{2}, Table[Floor[2^(2^n)/10^Floor[Log10[2^(2^n)]]], {n, 27}]] (* Stefano Spezia, Aug 10 2023 *)

Prog

(Python)
def A364837(n): return int(str(1<<(1<<n))[0]) # Chai Wah Wu, Sep 14 2023

Crossrefs

Cf. A000030, A001146, A362004, A364789, A364855.

Sequence in context: A057176 A194671 A331696 * A333651 A131398 A249307

Adjacent sequences: A364834 A364835 A364836 * A364838 A364839 A364840

Keyword

nonn,base

Author

Marco Ripà, Aug 10 2023

Extensions

More terms from Jinyuan Wang, Aug 10 2023

Status

approved