A391434 - OEIS

%I #14 Jan 20 2026 14:58:57

%S 4,6,8,9,12,16,22,27,33,34,35,36,38,39,44,45,46,48,49,52,54,58,62,64,

%T 66,69,72,75,78,81,85,87,88,92,94,96,102,104,106,108,111,114,115,116,

%U 117,121,122,123,125,128,134,136,138,141,142,144,146,148,152,153

%N Composite numbers (not multiples of 10) whose (radix-10) constant congruence speed equals the maximum of the constant congruence speeds of all their prime factors.

%C For the definition of "constant congruence speed", see A373387 and Def. 1.2 (and also Def. 1.1) of "Number of stable digits of any integer tetration" in Links (for all positive integers m > 1 and not a multiple of 10, this corresponds to A373387(m)).

%C If the product of two positive integers m' and m'' is not divisible by 10, then the constant congruence speed of m'*m'' is necessarily greater than or equal to the minimum of the constant congruence speeds of m' and m'' (see Equation 2.4 of "A Compact Notation for Peculiar Properties Characterizing Integer Tetration" in Links).

%C By definition, this sequence contains no prime number.

%D Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6

%H Marco Ripà, <a href="https://doi.org/10.7546/nntdm.2021.27.4.43-61">The congruence speed formula</a>, Notes on Number Theory and Discrete Mathematics, 2021, 27(4), 43-61.

%H Marco Ripà and Gabriele Di Pietro, <a href="https://doi.org/10.5281/zenodo.15276824">A Compact Notation for Peculiar Properties Characterizing Integer Tetration</a>, Zenodo, 2025.

%H Marco Ripà and Luca Onnis, <a href="https://doi.org/10.7546/nntdm.2022.28.3.441-457">Number of stable digits of any integer tetration</a>, Notes on Number Theory and Discrete Mathematics, 2022, 28(3), 441-457.

%e a(2) = 6 since the constant congruence speed of 6 is 1, the constant congruence speed of 2 is 1, the constant congruence speed of 3 is 1, and 1 equals max{1,1}.

%o (Python)

%o def upto(n):

%o     s=[]

%o     for k in range(4, n+1):

%o         if k%10==0:

%o             continue

%o         Vk=A373387(k)

%o         if Vk is None:

%o             continue

%o         pf=factorint(k)

%o         if sum(pf.values())==1:

%o             continue

%o         maxVp=0

%o         for p, e in pf.items():

%o             Vp=A373387(p)

%o             if Vp is not None and Vp>maxVp:

%o                 maxVp=Vp

%o         if Vk==maxVp:

%o             s.append(k)

%o     return s

%o print(upto(10000))

%Y Cf. A317905, A373387, A389432, A389979, A389980, A389981, A390320, A392231, A392233.

%Y Subsequence of A067251.

%K nonn,base

%O 1,1

%A _Marco Ripà_ and _Gabriele Di Pietro_, Jan 12 2026