A352301 a(n) is the n-th-to-last digit of A007013(n + 1).

7, 2, 7, 3, 7, 6, 7, 5, 8, 2, 3, 6, 8, 0, 3, 0, 5, 1, 6, 0, 0, 4, 4, 2, 5, 3, 1, 0, 0, 0, 1, 8, 4, 2, 3, 1, 7, 2, 8, 6, 1, 9, 9, 0, 3, 6, 9, 7, 4, 1, 1, 9, 5, 4, 8, 7, 6, 7, 2, 2, 2, 7, 5, 7, 6, 5, 5, 6, 0, 0, 3, 9, 8, 7, 6, 3, 8, 2, 3, 4, 7, 2, 2, 4, 4, 7

Offset: 1

Author

Davis Smith, Mar 11 2022

Keywords

• nonn
• base
• easy

Comments

Although the sequences for the most significant digits of Mersenne numbers, A000225, are not cyclic (the most significant is not cyclic, the second most is not, etc.), the sequences for the least significant digits are. For example, if p == 3 (mod 4), then A000225(p) == 7 (mod 10). Since A007013(n + 1) = A000225(A007013(n)) and A007013(1) == 3 (mod 4), all subsequent values will be congruent to 7 (mod 10). Similarly, if p == 7 (mod 20), A000225(p) == 27 (mod 100). In general, if p == x (mod A005054(n)), then A000225(p) == A000225(x) (mod 10^n).

There are many primes of the form Sum_{i=1..n} a(i)*10^(i - 1). The largest known is for n = 7032 (it is 7032 digits long).

Links

• Davis Smith, Table of n, a(n) for n = 1..7032

Crossrefs

Cf. A000225, A005054, A007013.

Programs

PARI

A352301_vec(n)=my(N=7,m=0);while(m
				

Formula

a(n) = floor(A007013(n + 1)/(10^(n - 1))) (mod 10).

A007013(n + 1) == Sum_{i=1..n} a(i)*10^(i - 1) (mod 10^n).