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
Examples
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
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)
- Shyam Sunder Gupta, Cab and Vampire Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 20, 499-512.
- Gordon Hamilton, Three integer sequences from recreational mathematics, Video (2013).
- Sean A. Irvine, Java program (github)
Programs
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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
Extensions
Edited by N. J. A. Sloane, Jan 03 2009
Comments