OFFSET
1,1
COMMENTS
Numbers that are the concatenation (in increasing order) of three consecutive primes and are the product of three primes, counted with multiplicity.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 434753 is a term because it is the concatenation of the consecutive primes 43, 47 and 53 and 434753 = 11^2 * 3593 is the product of three primes, counted with multiplicity.
MAPLE
cat3:= proc(a, b, c)
(a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c
end proc:
select(t ->numtheory:-bigomega(t)=3, [seq(cat3(ithprime(i), ithprime(i+1), ithprime(i+2)), i=1..100)]);
MATHEMATICA
p3[p_]:=FromDigits[Join[IntegerDigits[Prime[p]], IntegerDigits[Prime[p+1]], IntegerDigits[Prime[p+2]]]]; Select[Array[p3, 100], PrimeOmega[#]==3&] (* James C. McMahon, Jun 09 2025 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Will Gosnell and Robert Israel, May 23 2025
STATUS
approved