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A061762
a(n) = (sum of digits of n) + (product of digits of n).
16
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
0,2
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
FORMULA
a(n) = A007953(n) + A007954(n).
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
See A130858 for the smallest inverse.
Sequence in context: A088133 A115299 A076312 * A136614 A245627 A097586
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