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A382748 Primitive exponents for the greedy convolution of length 4.

%I A382748 #26 May 14 2025 13:27:31
%S A382748 1,5,6,7,8,9,11,13,17,19,23,25,27,29,30,31,32,35,36,37,40,41,42,43,45,
%T A382748 47,48,49,53,55,56,59,61,63,65,66,67,71,73,77,78,79,83,85,88,89,91,95,
%U A382748 97,99,101,102,103,104,107,109,113,114,115,117,119,121,125,127,131,133,135,136,137,138,139
%N A382748 Primitive exponents for the greedy convolution of length 4.
%C A382748 Integers n such that p^n is primitive for the "greedy convolution of length 4" when p is a prime number.
%C A382748 Smallest elements in the blocks of the greedy partition of the positive integers into parts of length at most 4.
%C A382748 First column of A382747.
%C A382748 Strict definition:
%C A382748 Form an infinite rooted tree T on the nonnegative integers in the following way.
%C A382748 1. 0 is the root
%C A382748 2. Form a branch 0 - 1 - 2 -3 - 4
%C A382748 3. Proceed inductively. Add n to end of an existing branch as either
%C A382748   0 - k=n
%C A382748   0 - k - 2k=n
%C A382748   0 - k - 2k - 3k=n
%C A382748   0 - k - 2k - 3k - 4k=n
%C A382748 with a preference for smaller k.
%C A382748 The primitive elements are the integers at distance one from the root.
%H A382748 Jan Snellman, <a href="/A382748/b382748.txt">Table of n, a(n) for n = 1..2598</a>
%H A382748 W. Narkiewicz, <a href="https://eudml.org/doc/209799">On a class of arithmetical convolutions</a>, Colloq. Math. 10, 1963, pp 81--94.
%H A382748 Jan Snellman, <a href="https://arxiv.org/abs/2504.02795">Greedy Regular Convolutions</a>, arXiv:2504.02795 [math.NT], 2025.
%e A382748 Up to n=15 the branches of the aforementioned tree looks like
%e A382748   0 - 1 - 2 - 3 - 4
%e A382748   0 - 5 - 10 - 15
%e A382748   0 - 6 - 12
%e A382748   0 - 7 - 14
%e A382748   0 - 8
%e A382748   0 - 9
%e A382748   0 - 11
%e A382748   0 - 13
%e A382748 so the primitive elements <= 15 are 1, 5, 6, 7, 8, 9, 11, 13.
%o A382748 (SageMath) # See A382747.
%Y A382748 First column of A382747.
%Y A382748 Cf. A121537.
%K A382748 nonn,easy
%O A382748 1,2
%A A382748 _Jan Snellman_, Apr 24 2025