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A317903 a(n) = A038394(n)^^A038394(n) (mod 10^len(A038394(n))), where ^^ indicates tetration or hyper-4 (e.g., 3^^4=3^(3^(3^3))). 7
4, 76, 176, 4176, 314176, 91314176, 891314176, 80891314176, 88080891314176, 5288080891314176, 705288080891314176, 10705288080891314176, 2410705288080891314176, 912410705288080891314176, 42912410705288080891314176, 9242912410705288080891314176, 989242912410705288080891314176 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..17.

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

Cf. A038394, A068670, A171882 (tetration), A317824.

Sequence in context: A100323 A262073 A067921 * A101718 A094160 A045996

Adjacent sequences:  A317900 A317901 A317902 * A317904 A317905 A317906

KEYWORD

nonn,base

AUTHOR

Marco Ripà, Aug 10 2018

EXTENSIONS

More terms from Jinyuan Wang, Aug 30 2020

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)