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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.

Contents

MMS numbers under 1000

References

External links

MMS numbers under 1000

We refer to ''n'' in the pair (''n'', ''n'' + 1) as a Maris-McGwire-Sosa number (or MMS number for short). Here are all the MMS numbers less than 1000:
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

References

1. Adam Spencer's Book of Numbers, Adam Spencer, , , Thunder's Mouth Press, 2004,

External links

★ Mike Keith. Maris-McGwire-Sosa Numbers.

★ Ivars Peterson. MathTrek - Home Run Numbers.

★ Hans Havermann. Maris-McGwire-Sosa 7-tuples, 8-tuples, & 9-tuples

★ Sequence , and in OEIS.