Corpus ID: 216642194

Three Cousins of Recamán's Sequence

  title={Three Cousins of Recam{\'a}n's Sequence},
  author={Max A. Alekseyev and Joseph Samuel Myers and Richard Schroeppel and Scott R. Shannon and N. J. A. Sloane and Paul Zimmermann},
  journal={arXiv: Number Theory},
Although 10^230 terms of Recaman's sequence have been computed, it remains a mystery. Here three distant cousins of that sequence are described, one of which is also mysterious. (i) {A(n), n >= 3} is defined as follows. Start with n, and add n+1, n+2, n+3, ..., stopping after adding n+k if the sum n + (n+1) + ... + (n+k) is divisible by n+k+1. Then A(n)=k. We determine A(n) and show that A(n) = 1} is a multiplicative analog of {A(n)}. Start with n, and successively multiply by n+1, n+2… Expand

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