OFFSET
0,2
COMMENTS
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
REFERENCES
S. Parmeswaran, S+P numbers, Mathematics Informatics Quarterly, Vol. 9, No. 3 (Sep 1999), Bulgaria.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
EXAMPLE
a(14) = 1+4 + 1*4 = 9.
MAPLE
read("transforms") :
A061762 := proc(n)
digsum(n)+A007954(n) ;
end proc: # R. J. Mathar, Aug 13 2012
MATHEMATICA
Table[Plus @@ IntegerDigits[n] + Times @@ IntegerDigits[n], {n, 0, 75}] (* Jayanta Basu, Apr 05 2013 *)
PROG
(PARI) SumD(x)= { s=0; while (x>9, s=s+x-10*(x\10); x=x\10); return(s + x) }
ProdD(x)= { p=1; while (x>9, p=p*(x-10*(x\10)); x=x\10); return(p*x) }
{ for (n=0, 1000, write("b061762.txt", n, " ", SumD(n) + ProdD(n)) ) } \\ Harry J. Smith, Jul 27 2009
(PARI) a(n) = if (n==0, 0, my(d=digits(n)); vecsum(d) + vecprod(d)); \\ Michel Marcus, Oct 29 2019, Jan 03 2020
(Python)
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
(Magma) [0] cat [&+Intseq(n)+&*Intseq(n): n in [1..80]]; // Vincenzo Librandi, Jan 03 2020
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, May 20 2001
EXTENSIONS
Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Matthew Conroy, May 23 2001
STATUS
approved