A367975 - OEIS

A367975

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

28, 40, 54, 78, 88, 102, 112, 138, 174, 208, 220, 222, 258, 270, 280, 304, 306, 318, 340, 348, 350, 352, 364, 366, 378, 414, 438, 460, 462, 474, 490, 496, 498, 520, 532, 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

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..60.

Farid Jokar, On the differences between Zumkeller and K-layered numbers, arXiv:1902.02168 [math.NT], 2019.

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

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

CROSSREFS

Cf. A083207.

Sequence in context: A216594 A324858 A084807 * A184032 A383939 A361855

Adjacent sequences: A367972 A367973 A367974 * A367976 A367977 A367978

KEYWORD

nonn

AUTHOR

Duc Van Khanh Tran, Dec 06 2023

STATUS

approved