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

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, 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, 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

Offset: 1

Author

Frank M Jackson, Apr 01 2020

Keywords

• nonn

Comments

Conjecture: For any prime number p there exists a positive integer k such that k*p is an Ulam number.

Examples

			a(3) = 29 because 5*29 gives the Ulam number 145 and this is the smallest Ulam number divisible by 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Ulam Sequence.
• Wikipedia, Ulam number.

Crossrefs

Cf. A002858, A322372.

Programs

Mathematica

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