Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.4 |

Institute of Advanced Study

Princeton, NJ 08540

USA

Norman E. Frankel

School of Physics

University of Melbourne

Victoria 3010

Australia

Anthony J. Guttmann

School of Mathematics and Statistics

The University of Melbourne

Victoria 3010

Australia

**Abstract:**

We define SanD (__S__um and __D__ifference) numbers as ordered pairs (*p*, *q*)
such that the digital sum *s*_{10}(*pq*) = *q* − *p* = Δ > 0. We consider
both the decimal and the binary cases in detail, and other bases more
superficially. If both *p* and *q* are prime numbers,
we refer to SanD primes.
For SanD primes, we prove that, with one exception, notably
the pair (2,7), the differences Δ = *q*−*p* = 14+18*k*, *k*=0,1,2,... .

Received April 17 2019; revised version received July 22 2019; January 7 2020.
Published in *Journal of Integer Sequences*,
February 24 2020.

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