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

Author

Eric W. Weisstein

Keywords

• nonn
• base

Comments

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

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

Examples

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

References

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

Links

• 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.

Crossrefs

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

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