- Maris-McGwire-Sosa pair
In
recreational mathematics , Maris-McGwire-Sosa pairs or MMS pairs are two consecutivenatural number s such that adding each number's digits (inbase 10 ) to the digits of itsprime 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 playersMark McGwire andSammy Sosa both hit their 62ndhome run s for the season, passing the old record of 61, held byRoger Maris . American engineer Mike Keith noticed this property of these numbers and named pairs of numbers like this MMS pairs. [cite book
url=http://books.google.com/books?id=cCqtEk_3INsC&pg=RA1-PA62&ots=quTFDcnfOR&dq=Maris-McGwire-Sosa+pair&sig=6ybNyevO86QfnmtYGyy7Oaw1FHQ
title=Adam Spencer's Book of Numbers
author=Adam Spencer
year=2004
publisher=Thunder's Mouth Press] Except for the origin of the name, MMS pairs are unrelated to baseball. This is also the case forRuth-Aaron pair s 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 OEIS|id=A045759.
References
External links
*Mike Keith. [http://users.aol.com/s6sj7gt/maris.htm Maris-McGwire-Sosa Numbers] .
*Ivars Peterson. [http://www.maa.org/mathland/mathtrek_9_28_98.html MathTrek - Home Run Numbers] .
*Hans Havermann. [http://chesswanks.com/pxp/seven.html Maris-McGwire-Sosa 7-tuples, 8-tuples, & 9-tuples]
*Sequence OEIS2C|id=A045759, OEIS2C|id=A045760 and OEIS2C|id=A039945 inOEIS .
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