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

1,3

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Ulam Sequence.

Wikipedia, Ulam number.

Example

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

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

Crossrefs

Cf. A002858, A322372.

Sequence in context: A040828 A040829 A040830 * A040823 A040824 A040825

Adjacent sequences: A333673 A333674 A333675 * A333677 A333678 A333679

Keyword

nonn

Author

Frank M Jackson, Apr 01 2020

Status

approved