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 A020342 Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits. 15
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)