A020342 Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits.

126, 153, 688, 1206, 1255, 1260, 1395, 1435, 1503, 1530, 1827, 2187, 3159, 3784, 6880, 10251, 10255, 10426, 10521, 10525, 10575, 11259, 11439, 11844, 11848, 12006, 12060, 12384, 12505, 12546, 12550, 12595, 12600, 12762, 12768, 12798, 12843, 12955, 12964

Offset

1,1

Comments

Nontrivial means that there must be at least two factors.

For any a(n), 10*a(n) is also in the sequence, and also in A144563. - M. F. Hasler, Nov 01 2021

References

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

Links

Ely Golden, Table of n, a(n) for n = 1..1000 (corrected by Sean A. Irvine)

Ely Golden, Sympy program for generating vampire numbers (definition 1)

Gordon Hamilton, Three integer sequences from recreational mathematics, Video (2013).

Sean A. Irvine, Java program (github)

Example

1395 = 31*9*5, so 1395 is a term.
179739 = 7 * 9 * 9 * 317 so 179739 is a term. - Sean A. Irvine, Feb 28 2023

Prog

(PARI) is_A020342(n, m=0, D=vecsort(digits(n)))={ if(m && n >= m && vecsort(digits(n))==D, 1, #D<3, m && (D[1]>=m && vecprod(D)==n), n >= m^2, my(S=Set(D), i, C); fordiv(n, f, f < m && next; f*f > n && break; setminus(Set(digits(f)), S) && next; C=D; foreach(digits(f), d, if(i=vecsearch(C, d), C=C[^i], next(2))); C && is_A020342(n\f, f, C) && return(1)))} \\ See A144563 for a function counting the multiplicity of the representation. - M. F. Hasler, Nov 01 2021

Crossrefs

Closely related: A014575, A080718, A280928, A048936, A144563.

Sequence in context: A025388 A025389 A025380 * A179482 A009944 A203566

Adjacent sequences: A020339 A020340 A020341 * A020343 A020344 A020345

Keyword

nonn,base

Author

David W. Wilson

Extensions

Edited by N. J. A. Sloane, Jan 03 2009

Status

approved