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A061762 a(n) = (sum of digits of n) + (product of digits of n). 14
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 (list; graph; refs; listen; history; text; internal format)
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 < 10^21. - Chai Wah Wu, Aug 14 2017

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

(Python)

from operator import mul

from functools import reduce

def A067162(n):

    a = [int(d) for d in str(n)]

    return sum(a)+reduce(mul, a) # Chai Wah Wu, Aug 14 2017

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

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Last modified September 20 16:05 EDT 2017. Contains 292276 sequences.