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Zumkeller numbers q such that q+2 is also a Zumkeller number.
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%I #18 Jan 19 2024 08:19:31

%S 28,40,54,78,88,102,112,138,174,208,220,222,258,270,280,304,306,318,

%T 340,348,350,352,364,366,378,414,438,460,462,474,490,496,498,520,532,

%U 544,550,558,570,580,606,616,618,640,642,678,700,702,726,760,768,810,820,832,834,858,868,894,910,918

%N Zumkeller numbers q such that q+2 is also a Zumkeller number.

%C Somu et al. (2023) proved that there exist infinitely many strings of consecutive Zumkeller numbers of arbitrary length. This result implies that there are infinitely many Zumkeller numbers q such that q+2 is also a Zumkeller number.

%H Farid Jokar, <a href="https://arxiv.org/abs/1902.02168">On the differences between Zumkeller and K-layered numbers</a>, arXiv:1902.02168 [math.NT], 2019.

%H Yuejian Peng and K. P. S. Bhaskara Rao, <a href="https://doi.org/10.1016/j.jnt.2012.09.020">On Zumkeller numbers</a>, Journal of Number Theory, 133(4), 2013, 1135-1155.

%H Sai Teja Somu, Andrzej Kukla, and Duc Van Khanh Tran, <a href="https://arxiv.org/abs/2310.14149">Some results on Zumkeller numbers</a>, arXiv:2310.14149 [math.NT], 2023.

%e 28 and 40 are in the sequence because 30 and 42 are also Zumkeller numbers.

%Y Cf. A083207.

%K nonn

%O 1,1

%A _Duc Van Khanh Tran_, Dec 06 2023