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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). 3

%I #23 Jul 14 2021 10:05:39

%S 7,14,43,50,61,63,67,80,84,118,122,134,137,163,196,212,213,224,241,

%T 273,274,277,279,283,351,352,373,375,390,398,421,457,462,474,475,489,

%U 495,510,516,523,526,537,547,555,558,577,584,590,592,616,638,644,660,673,687,691

%N 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).

%C 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

%H Amiram Eldar, <a href="/A045759/b045759.txt">Table of n, a(n) for n = 1..10000</a>

%H Mike Keith, <a href="http://www.cadaeic.net/maris.htm">Maris-McGwire-Sosa Numbers</a>, 1998.

%H Ivars Peterson, <a href="https://web.archive.org/web/20130702054338/https://www.maa.org/mathland/mathtrek_9_28_98.html">Home Run Numbers</a>, MathTrek, 1998.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Maris%E2%80%93McGwire%E2%80%93Sosa_pair">Maris-McGwire-Sosa pair</a>.

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

%t 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 *)

%o (Python)

%o from sympy import factorint

%o def sd(n): return sum(map(int, str(n)))

%o def f(n): return sd(n) + sum(sd(p)*e for p, e in factorint(n).items())

%o def ok(n): return f(n) == f(n+1)

%o print(list(filter(ok, range(692)))) # _Michael S. Branicky_, Jul 14 2021

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

%K nonn,base

%O 1,1

%A Mike Keith (domnei(AT)aol.com)

%E Corrected and extended by _David W. Wilson_

%E Offset corrected by _Amiram Eldar_, Nov 24 2019

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)