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

0,2

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

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

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

See A130858 for the smallest inverse.

Sequence in context: A088133 A115299 A076312 * A136614 A245627 A097586

Adjacent sequences: A061759 A061760 A061761 * A061763 A061764 A061765

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