A359491 - OEIS

%I #26 Jan 28 2023 15:46:49

%S 2,3,5,7,333,23532,33165,77322,175175,232152,321372,373212,515375,

%T 712236,2249232,2321232,2971332,3372138,3611322,4313331,5773131,

%U 12322332,23147124,42323112,72325232,113338575,123221232,132232224,172232112,212322912,221437272,273233331

%N 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.

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

%C 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.

%H John R Phelan, <a href="/A359491/a359491.txt">Java program</a>

%e 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.

%e 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.

%o (Python)

%o from sympy import factorint

%o def ok(n): return sorted(str(n)) == sorted(s[0] for s in map(str, factorint(n, multiple=True)))

%o print([k for k in range(1, 10**5) if ok(k)]) # _Michael S. Branicky_, Jan 08 2023

%o (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

%o (Java) See Links

%Y Cf. A115024.

%K nonn,base

%O 1,1

%A _John R Phelan_, Jan 02 2023