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A061762 a(n) = (sum of digits of n) + (product of digits of n).

%I A061762 #62 Dec 04 2024 17:51:25
%S A061762 0,2,4,6,8,10,12,14,16,18,1,3,5,7,9,11,13,15,17,19,2,5,8,11,14,17,20,
%T A061762 23,26,29,3,7,11,15,19,23,27,31,35,39,4,9,14,19,24,29,34,39,44,49,5,
%U A061762 11,17,23,29,35,41,47,53,59,6,13,20,27,34,41,48,55,62,69,7,15,23,31,39,47
%N A061762 a(n) = (sum of digits of n) + (product of digits of n).
%C A061762 Fixed points a(m) = m are m = {0, 19, 29, 39, 49, 59, 69, 79, 89, 99}. Is this list complete? - _Zak Seidov_, Aug 22 2007
%C A061762 The above list of fixed points is complete. If a(m) = m, then m < 10^21 and there are no other fixed points below 10^21. - _Chai Wah Wu_, Aug 14 2017
%C A061762 All numbers are in this sequence. Proof: One can create a number m whose digital sum is any number p and one can create a number k by concatenating digit "0" to m. Then this number k will be a term. - _Metin Sariyar_, Oct 29 2019
%D A061762 S. Parmeswaran, S+P numbers, Mathematics Informatics Quarterly, Vol. 9, No. 3 (Sep 1999), Bulgaria.
%H A061762 Harry J. Smith, <a href="/A061762/b061762.txt">Table of n, a(n) for n = 0..1000</a>
%F A061762 a(n) = A007953(n) + A007954(n).
%e A061762 a(14) = 1+4 + 1*4 = 9.
%p A061762 read("transforms") :
%p A061762 A061762 := proc(n)
%p A061762     digsum(n)+A007954(n) ;
%p A061762 end proc: # _R. J. Mathar_, Aug 13 2012
%t A061762 Table[Plus @@ IntegerDigits[n] + Times @@ IntegerDigits[n], {n, 0, 75}] (* _Jayanta Basu_, Apr 05 2013 *)
%o A061762 (PARI) a(n) = if (n==0, 0, my(d=digits(n)); vecsum(d) + vecprod(d)); \\ _Michel Marcus_, Oct 29 2019, Jan 03 2020
%o A061762 (Python)
%o A061762 from operator import mul
%o A061762 from functools import reduce
%o A061762 def A061762(n):
%o A061762     a = [int(d) for d in str(n)]
%o A061762     return sum(a)+reduce(mul,a) # _Chai Wah Wu_, Aug 14 2017
%o A061762 (Magma) [0] cat [&+Intseq(n)+&*Intseq(n): n in [1..80]];// _Vincenzo Librandi_, Jan 03 2020
%Y A061762 Cf. A007953, A007954, A061763, A038366, A074871.
%Y A061762 See A130858 for the smallest inverse.
%K A061762 nonn,base,easy
%O A061762 0,2
%A A061762 _Amarnath Murthy_, May 20 2001
%E A061762 Corrected and extended by Larry Reeves (larryr(AT)acm.org) and _Matthew Conroy_, May 23 2001