A074871 -id:A074871 - cp's OEIS frontend

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

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, 23, 26, 29, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 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

Offset: 0

Amarnath Murthy, May 20 2001

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
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
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

			a(14) = 1+4 + 1*4 = 9.

S. Parmeswaran, S+P numbers, Mathematics Informatics Quarterly, Vol. 9, No. 3 (Sep 1999), Bulgaria.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A007953, A007954, A061763, A038366, A074871.

See A130858 for the smallest inverse.

[0] cat [&+Intseq(n)+&*Intseq(n): n in [1..80]];// Vincenzo Librandi, Jan 03 2020

read("transforms") :
A061762 := proc(n)
    digsum(n)+A007954(n) ;
end proc: # R. J. Mathar, Aug 13 2012

Table[Plus @@ IntegerDigits[n] + Times @@ IntegerDigits[n], {n, 0, 75}] (* Jayanta Basu, Apr 05 2013 *)

a(n) = if (n==0, 0, my(d=digits(n)); vecsum(d) + vecprod(d)); \\ Michel Marcus, Oct 29 2019, Jan 03 2020

from operator import mul
from functools import reduce
def A061762(n):
    a = [int(d) for d in str(n)]
    return sum(a)+reduce(mul,a) # Chai Wah Wu, Aug 14 2017

a(n) = A007953(n) + A007954(n).

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Matthew Conroy, May 23 2001

A171772 Number of steps needed to reach a prime when the map S(n)+M(n) is applied to n, or -1 if a prime is never reached. Here S(n) and M(N) mean the sum and the product of the digits of n in base 10.

Original entry on oeis.org

1, 0, 0, 3, 0, 2, 0, 2, 2, 2, 0, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 3, 0, 4, 1, 2, 1, 3, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, -1, 4, 0, 4, 0, 5, 1, 2, 0, 6, -1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 3, 0, 2, 2, 2, 1, 7, 0, 3, -1, 1, 0, 1, 0, -1, 1, 3, 3, 1, 0, 3

Offset: 1

R. J. Mathar, Oct 12 2010

a(n)=0 if n is a prime.

			a(4)=3 because 4->8->16->13 is prime.
a(39)=-1 because 39 -> 39 ->39 ... never reaches a prime.
a(49)=-1 because 49 -> 49 ->49 ... never reaches a prime.
a(69)=-1 because 69 -> 69 ->69 ... never reaches a prime.
a(74)=-1 because 74 -> 39 ->39 ... never reaches a prime.
a(28)=3 because 28 ->26 ->20 ->2.

Robert Israel, Table of n, a(n) for n = 1..10000

A variant of A074871.

Cf. A007954, A053837, A061762.

f:= proc(n) local L;
  L:= convert(n,base,10);
  convert(L,`+`)+convert(L,`*`);
end proc:
g:= proc(n) option remember; local v,w;
     if n::prime then return 0 fi;
     v:= f(n);
     if v = n then return -1 fi;
     w:= procname(v);
     if w = -1 then -1 else w+1 fi
end proc:
map(g, [$1..100]); # Robert Israel, Nov 03 2019

cp's OEIS Frontend

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

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