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. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games. In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an The decimal ( base ten or occasionally denary) Numeral system has ten as its base.

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. Baseball is a Bat-and-ball Sport played between two teams of nine players each Mark David McGwire (born October 1 1963 in Pomona California) is a former professional baseball player who played the majority of his Major League career with the Samuel Peralta Sosa (born November 12, 1968 in San Pedro de Macorís, Dominican Republic) is a Right fielder who is currently Roger Eugene Maris ( September 10 1934 &ndash December 14 1985) was an American Right fielder in Major League Baseball 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. In Mathematics, a Ruth-Aaron pair consists of two Consecutive integers (e

## 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). The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences

## References

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