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.

2295, 29625, 869227, 24612989369, 989252839643, 475851922819895, 2766613478748294, 383649822198994888719136, 753247689895391625667326763984815199

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

a(10) > 10^76. - Michael S. Branicky, Jul 31 2024

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: A349085 A274359 A306871 * 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