A225864 Composite numbers for which both sum and product of digits are primes.
12, 21, 115, 511, 1112, 1121, 1211, 11711, 13111, 17111, 31111, 71111, 111112, 121111, 211111, 1111115, 1111117, 1111171, 1111511, 1115111, 1151111, 1511111, 1711111, 5111111, 7111111, 111111115, 111111151, 111111311, 111111511, 111115111, 111131111, 111151111
Offset: 1
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
d[n_] := IntegerDigits[n]; t={}; Do[If[!PrimeQ[n] && PrimeQ[Plus@@(x=d[n])] && PrimeQ[Times@@x], AppendTo[t,n]], {n,2*10^6}]; t Select[Range[72*10^5],CompositeQ[#]&&AllTrue[{Total[IntegerDigits[#]],Times@@ IntegerDigits[ #]},PrimeQ]&] (* The program generates the first 25 terms of the sequence. *) (* Harvey P. Dale, May 24 2024 *) -
Python
from _future_ import division from sympy import isprime A225864_list = [] for l in range(1,20): plist, q = [p for p in [2,3,5,7] if isprime(l-1+p)], (10**l-1)//9 for i in range(l): for p in plist: r = q+(p-1)*10**i if not isprime(r): A225864_list.append(r) # Chai Wah Wu, Aug 15 2017
Extensions
Extended by T. D. Noe, May 18 2013