A309697 a(n) is the digit that precedes the last nonzero digit of n^n.

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

Offset: 1

Author

Michel Marcus, Aug 13 2019

Keywords

• nonn
• base

Comments

Chu proves that the constant 0.00252541801... is transcendental.

Links

• Hung Viet Chu, New Transcendental Numbers from Certain Sequences, arXiv:1908.03855 [math.NT], 2019.

Crossrefs

Cf. A056849.

Programs

Mathematica

a[n_] := Floor[PowerMod[n/10^IntegerExponent[n, 10], n, 100]/10]; Array[a, 100] (* Giovanni Resta, Aug 13 2019 *)

PARI

a(n) = {my(d=digits(n^n)); forstep (k=#d, 1, -1, if (d[k], if (k==1, return (0)); return (d[k-1]));); return(0);}