A359491 Numbers k with the property that the set of decimal digits of k matches the set of first digits of the prime factors of k.

2, 3, 5, 7, 333, 23532, 33165, 77322, 175175, 232152, 321372, 373212, 515375, 712236, 2249232, 2321232, 2971332, 3372138, 3611322, 4313331, 5773131, 12322332, 23147124, 42323112, 72325232, 113338575, 123221232, 132232224, 172232112, 212322912, 221437272, 273233331

Offset: 1

Author

John R Phelan, Jan 02 2023

Keywords

• nonn
• base

Comments

Analogous to an acrostic, in which the first digit of each prime factor also forms the number itself.

There could also be a sequence based on the set of decimal digits of k matching the set of last digits of the prime factors of k; 373212 = 2*2*3*3*7*1481 and 73222329312 = 2*2*2*2*2*3*3*11*79*307*953 are examples of numbers in both sequences.

Examples

			a(5)=333 has prime factors 3*3*37, the first digits of which are 3, 3 and 3, matching the set of digits in 333.
a(10)=232152 has prime factors 2*3*2*17*569*2, the first digits of which are 2, 3, 2, 1, 5 and 2, matching the set of digits in 232152.
		

Links

• John R Phelan, Java program

Crossrefs

Cf. A115024.

Programs

Java

See Links

PARI

is(n) = { my (d=digits(n), f=factor(n)); #d==bigomega(f) && vecsort(d) == vecsort(concat(vector(#f~, k, vector(f[k,2], z, digits(f[k,1])[1])))) } \\ Rémy Sigrist, Jan 28 2023

Python

from sympy import factorint
def ok(n): return sorted(str(n)) == sorted(s[0] for s in map(str, factorint(n, multiple=True)))
print([k for k in range(1, 10**5) if ok(k)]) # Michael S. Branicky, Jan 08 2023