A045759 Maris-McGwire numbers: numbers k such that f(k) = f(k+1), where f(k) = sum of digits of k + sum of digits of prime factors of k (including multiplicities).

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

Offset

1,1

Comments

Named "Maris-McGwire-Sosa Numbers" by Keith (1998) after the baseball players Roger Maris, Mark McGwire and Sammy Sosa. Both McGwire and Sosa hit their 62nd home runs for the season, breaking Maris's record of 61 (A006145 is a similarly named sequence). - Amiram Eldar, Jun 27 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mike Keith, Maris-McGwire-Sosa Numbers, 1998.

Ivars Peterson, Home Run Numbers, MathTrek, 1998.

Wikipedia, Maris-McGwire-Sosa pair.

Example

(61, 62) is such a pair, hence the name.

Mathematica

ds[n_] := Plus @@ IntegerDigits[n]; f[n_] := ds[n] + Total[(fi = FactorInteger[n])[[;; , 2]] *( ds /@fi[[;; , 1]])]; s={}; f1 = 1; Do[f2=f[n]; If[f1 == f2, AppendTo[s, n-1]]; f1 = f2, {n, 2, 700}]; s (* Amiram Eldar, Nov 24 2019 *)

Prog

(Python)
from sympy import factorint
def sd(n): return sum(map(int, str(n)))
def  f(n): return sd(n) + sum(sd(p)*e for p, e in factorint(n).items())
def ok(n): return f(n) == f(n+1)
print(list(filter(ok, range(692)))) # Michael S. Branicky, Jul 14 2021

Crossrefs

Cf. A006145 (Ruth-Aaron numbers), A039945.

Sequence in context: A189046 A098328 A062098 * A166637 A237686 A170918

Adjacent sequences: A045756 A045757 A045758 * A045760 A045761 A045762

Keyword

nonn,base

Author

Mike Keith (domnei(AT)aol.com)

Extensions

Corrected and extended by David W. Wilson

Offset corrected by Amiram Eldar, Nov 24 2019

Status

approved