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

1,1

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.

Links

Table of n, a(n) for n=1..32.

John R Phelan, Java program

Example

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.

Prog

(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
(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
(Java) See Links

Crossrefs

Cf. A115024.

Sequence in context: A052024 A052023 A052025 * A045336 A083183 A046477

Adjacent sequences: A359488 A359489 A359490 * A359492 A359493 A359494

Keyword

nonn,base

Author

John R Phelan, Jan 02 2023

Status

approved