A048937 Numbers n with an even number of digits, n = d_1 d_2 ... d_n, such that there are exactly three ways to partition the digits into two groups of size n/2, say f_1 ... f_{n/2} and g_1 ... g_{n/2}, such that n = f_1 ... f_{n/2} * g_1 ... g_{n/2}.

13078260, 107650322640, 113024597400, 119634515208, 134549287600, 135173486250, 138130447950, 146083269717, 150967233648, 216315684000, 221089445500, 315987404670, 463997983680, 472812953760, 10174695862032, 10178463985200, 10185571893960, 10476754939728, 10624657891320

Offset

1,1

Comments

f_{n/2} and g_{n/2} may not both be zero.

Vampire numbers (definition 2) having exactly three distinct pairs of fangs.

References

C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to Infinity. New York: Wiley, pp. 227-231, 1995.

Links

Table of n, a(n) for n=1..19.

Shyam Sunder Gupta, Cab and Vampire Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 20, 499-512.

Walter Schneider, Vampire numbers

Eric Weisstein's World of Mathematics, Vampire Number.

Example

13078260 = 1620*8073 = 1863*7020 = 2070*6318; 107650322640 = 153204*702660 = 140532*766020 = 200760*536214.

Crossrefs

Cf. A014575, A048933, ..., A048939.

Sequence in context: A237034 A210182 A210412 * A257269 A283274 A343083

Adjacent sequences: A048934 A048935 A048936 * A048938 A048939 A048940

Keyword

nonn,base,changed

Author

Eric W. Weisstein

Extensions

More terms found by Walter Schneider, Feb 11 2002 and communicated by Hans Havermann, Oct 10 2002

More terms from Jens Kruse Andersen, Dec 01 2002

Status

approved