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A061762
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a(n) = (sum of digits of n) + (product of digits of n).
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16
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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
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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S. Parmeswaran, S+P numbers, Mathematics Informatics Quarterly, Vol. 9, No. 3 (Sep 1999), Bulgaria.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A007953(n) + A007954(n).
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EXAMPLE
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a(14) = 1+4 + 1*4 = 9.
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MAPLE
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read("transforms") :
A061762 := proc(n)
digsum(n)+A007954(n) ;
end proc: # R. J. Mathar, Aug 13 2012
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MATHEMATICA
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Table[Plus @@ IntegerDigits[n] + Times @@ IntegerDigits[n], {n, 0, 75}] (* Jayanta Basu, Apr 05 2013 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,base,easy
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AUTHOR
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Amarnath Murthy, May 20 2001
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EXTENSIONS
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Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Matthew Conroy, May 23 2001
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STATUS
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approved
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