OFFSET
1,1
COMMENTS
For any n >= 2, a(n) (mod 10^len(A038394(n))) == a(n + 1) (mod 10^len(A038394(n))), where len(k) := number of digits in k. Assuming len(a(n))>1, this is a general property of every concatenated sequence with fixed rightmost digits (such as A014925 or A092447), as shown in Ripà's book "La strana coda della serie n^n^...^n".
REFERENCES
Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6
LINKS
Marco Ripà, On the Convergence Speed of Tetration, ResearchGate (2018).
FORMULA
a(n) = (p(n)_p(n-1)_p(n-2)_..._3_2)^^(p(n)_p(n-1)_p(n-2)_..._3_2) (mod 10^len(p(n)_p(n-1)_p(n-2)_..._3_2)), where len(k) := number of digits in k.
EXAMPLE
For n = 6, a(6) = 13117532^^13117532 (mod 10^8) == 91314176.
PROG
(PARI) tmod(b, n) = {if (b % n == 0, return (0)); if (b % n == 1, return (1)); if (gcd(b, n)==1, return (lift(Mod(b, n)^tmod(b, lift(znorder(Mod(b, n))))))); lift(Mod(b, n)^(eulerphi(n) + tmod(b, eulerphi(n)))); }
f(n) = fromdigits(concat([digits(p) | p<-Vecrev(primes(n))])); \\ A038394
a(n) = if (n==1, 4, my(x=f(n)); tmod(x, 10^#Str(x))); \\ Michel Marcus, Sep 12 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marco Ripà, Aug 10 2018
EXTENSIONS
More terms from Jinyuan Wang, Aug 30 2020
STATUS
approved