# Maris-McGwire-Sosa pair

In recreational mathematics, Maris-McGwire-Sosa pairs or MMS pairs are two consecutive natural numbers such that adding each number's digits (in base 10) to the digits of its prime factorization gives the same sum.

Thus 61 -> 6 + 1 (the sum of its digits) + 6 + 1 (since 61 is its prime factorization)

and 62 -> 6 + 2 (the sum of its digits) + 3 + 1 + 2 (since 31 × 2 is its prime factorization).

The above two sums are equal (= 14), so 61 and 62 form an MMS pair.

MMS pairs are so named because in 1998 the baseball players Mark McGwire and Sammy Sosa both hit their 62nd home runs for the season, passing the old record of 61, held by Roger Maris. American engineer Mike Keith noticed this property of these numbers and named pairs of numbers like this MMS pairs.[1] Except for the origin of the name, MMS pairs are unrelated to baseball. This is also the case for Ruth-Aaron pairs which have a similar mathematical property and had earlier been named after baseball players who set home run records.

MMS numbers under 1000

n in the pair (n, n + 1) is called a Maris-McGwire-Sosa number (or MMS number for short). The MMS numbers less than 1000 are:

7, 14, 43, 50, 61, 63, 67, 80, 84, 118, 122, 134, 137, 163, 196, 212, 213, 224, 241, 273, 274, 277, 279, 283, 351, 352, 373, 375, 390, 398, 421, 457, 462, 474, 475, 489, 495, 510, 516, 523, 526, 537, 547, 555, 558, 577, 584, 590, 592, 616, 638, 644, 660, 673, 687, 691, 731, 732, 743, 756, 774, 787, 797, 860, 871, 878, 895, 907, 922, 928, 944, 949, 953, 965, 985, 997 (sequence A045759 in OEIS).

References

1. ^ Adam Spencer (2004). Adam Spencer's Book of Numbers. Thunder's Mouth Press.