A368007 Positive integers which cannot be written as a sum of two Zumkeller numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

Offset

1,2

Comments

Somu et al. (2023) proved that all but finitely many positive integers can be written as a sum of two Zumkeller numbers. Therefore, this sequence is finite.

Links

Duc Van Khanh Tran, Table of n, a(n) for n = 1..1541

Yuejian Peng and K. P. S. Bhaskara Rao, On Zumkeller numbers, Journal of Number Theory, 133(4), 2013, 1135-1155.

Sai Teja Somu, Andrzej Kukla, and Duc Van Khanh Tran, Some results on Zumkeller numbers, arXiv:2310.14149 [math.NT], 2023.

Example

All positive integers less than 12 are in the sequence because the smallest sum of two Zumkeller numbers is 6+6=12.

Crossrefs

Cf. A083207.

Sequence in context: A357758 A255724 A285100 * A360553 A067340 A263837

Adjacent sequences: A368004 A368005 A368006 * A368008 A368009 A368010

Keyword

nonn,fini,full

Author

Duc Van Khanh Tran, Dec 07 2023

Status

approved