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A123911 Numbers n such that if you multiply the primes that are indexed by the digits of n and add the sum of digits of n you get n. 0
2295, 29625, 869227, 24612989369, 989252839643, 475851922819895, 2766613478748294, 383649822198994888719136, 753247689895391625667326763984815199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

As prime(0) is not defined, n may not contain any zero digits.

a(10) > 10^40. - Max Alekseyev, Feb 08 2010

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

2295 is in the sequence because prime(2)*prime(2)*prime(9)*prime(5) + sum of digits of 2295 = 3*3*23*11 + (2+2+9+5) = 2277 + 18 = 2295.

MATHEMATICA

fQ[n_] := ! MemberQ[IntegerDigits@n, 0] && Times @@ Prime@ IntegerDigits@n + Plus @@ IntegerDigits@n == n; Do[ If[fQ@n, Print@n], {n, 2*10^9}]

PROG

(PARI) { a(m) = forvec(v=vector(8, i, [0, m]), u=vector(9, i, if(i<9, v[i], m)-if(i>1, v[i-1], 0) ); t=prod(i=1, 9, prime(i)^u[i])+sum(i=1, 9, u[i]*i); s=eval(Vec(Str(t))); if(#s!=m, next); w=vector(9); for(j=1, #s, if(s[j], w[s[j]]++)); if(u==w, print(t)), 1) } /* m is the length */ \\ Max Alekseyev, Feb 08 2010

(Python)

from operator import mul

from functools import reduce

from itertools import combinations_with_replacement

A123911_list, plist = [], [0]+[prime(i) for i in range(1, 10)]

for l in range(1, 30):

    L = 10**(l-1)

    H = 10*L

    for c in combinations_with_replacement(range(1, 10), l):

        n = reduce(mul, [plist[i] for i in c]) + sum(c)

        if L <= n < H and sorted(int(d) for d in str(n)) == list(c):

            A123911_list.append(n) # Chai Wah Wu, Jan 02 2016

CROSSREFS

Sequence in context: A023323 A163513 A274359 * A126173 A083572 A270854

Adjacent sequences:  A123908 A123909 A123910 * A123912 A123913 A123914

KEYWORD

base,more,nonn

AUTHOR

Tanya Khovanova, Oct 28 2006

EXTENSIONS

a(4) and a(5) from Donovan Johnson, Apr 22 2008

a(6)-a(9) from Max Alekseyev, Feb 08 2010

STATUS

approved

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Last modified January 24 12:26 EST 2017. Contains 281237 sequences.