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A351741 Numbers k such that the concatenation of 1,2,...,k and the concatenation of k,k-1,...,1 have the same number of prime factors, counted with multiplicity.

%I A351741 #22 Mar 31 2022 22:00:13
%S A351741 1,3,4,5,7,10,13,16,23,26,31,32,37,39,51,54,56
%N A351741 Numbers k such that the concatenation of 1,2,...,k and the concatenation of k,k-1,...,1 have the same number of prime factors, counted with multiplicity.
%C A351741 Numbers k such that A001222(A007908(k)) = A001222(A000422(k)).
%e A351741 a(3) = 4 is a term because 1234 = 2*617 and 4321 = 29*149 each have two prime factors.
%p A351741 dcat:= (a,b) -> a*10(1+ilog10(b))+b:
%p A351741 a:= 1: b:= 1: R:= 1:
%p A351741 for n from 2 to 40 do
%p A351741 a:= dcat(n,a);
%p A351741 b:= dcat(b,n);
%p A351741 if numtheory:-bigomega(a) = numtheory:-bigomega(b) then R:= R,n fi
%p A351741 od:
%p A351741 R;
%t A351741 Select[Range[32], SameQ @@ PrimeOmega@{FromDigits@ Flatten@ #, FromDigits@ Flatten@ Reverse[#]} &@ IntegerDigits@ Range[#] &] (* _Michael De Vlieger_, Feb 17 2022 *)
%o A351741 (Python)
%o A351741 from sympy import primeomega
%o A351741 def afind(limit, startk=1):
%o A351741     k = startk
%o A351741     sk = "".join(str(i) for i in range(1, k))
%o A351741     skr = "".join(str(i) for i in range(k-1, 0, -1))
%o A351741     for k in range(startk, limit+1):
%o A351741         sk += str(k)
%o A351741         skr = str(k) + skr
%o A351741         if primeomega(int(sk)) == primeomega(int(skr)):
%o A351741             print(k, end=", ")
%o A351741 afind(23) # _Michael S. Branicky_, Feb 17 2022
%Y A351741 Cf. A000422, A001222, A007908, A048288.
%K A351741 nonn,base,more
%O A351741 1,2
%A A351741 _J. M. Bergot_ and _Robert Israel_, Feb 17 2022
%E A351741 a(17) from _Michael S. Branicky_, Feb 19 2022