2-Adic Congruences of Nörlund Numbers and of Bernoulli Numbers of the Second Kind Original Research Article

In this paper, we find simple 2-adic congruences mod 2[n/2]+1for the Nörlund numbersB(n)nand for the Bernoulli numbers of the second kindbn. These congruences improve F. T. Howardʹs mod 8 congruences (in“Applications of Fibonacci Numbers,” Vol. 5, pp. 355–366, Kluwer Academic, Dordrecht, 1993). We use recurrence relations to determine when our congruences are best possible and to obtain further information about the 2-adic expansions ofB(n)n/n! and ofbn.