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A333676 Least positive integer k such that k*prime(n) is an Ulam number (A002858).

%I A333676 #18 Feb 16 2025 08:33:59
%S A333676 1,1,29,4,1,1,6,2,3,3,2,4,2,6,1,1,3,12,6,7,3,4,13,4,1,13,2,21,12,3,16,
%T A333676 1,5,5,19,8,22,15,4,13,2,5,2,26,1,15,38,6,16,12,10,13,1,2,8,4,38,5,15,
%U A333676 205,2,5,10,31,4,6,16,8,31,20,5,7,2,4,4,18,3,3,4,1,3,8,1,2,10,8,15,12
%N A333676 Least positive integer k such that k*prime(n) is an Ulam number (A002858).
%C A333676 Conjecture: For any prime number p there exists a positive integer k such that k*p is an Ulam number.
%H A333676 Amiram Eldar, <a href="/A333676/b333676.txt">Table of n, a(n) for n = 1..10000</a>
%H A333676 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>.
%H A333676 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>.
%e A333676 a(3) = 29 because 5*29 gives the Ulam number 145 and this is the smallest Ulam number divisible by 5.
%t A333676 lst1 = ReadList["https://oeis.org/A002858/b002858.txt", {Number, Number}]; lst = {}; Do[n=1; While[!IntegerQ[k=lst1[[n]][[2]]/Prime[m]], n++]; AppendTo[lst, k], {m, 1, 100}]; lst
%Y A333676 Cf. A002858, A322372.
%K A333676 nonn
%O A333676 1,3
%A A333676 _Frank M Jackson_, Apr 01 2020