This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A207005 #12 Nov 22 2023 22:30:09 %S A207005 1,3,4,5,8,9,12,14,17,20,22,24,26,28,32,35,36,38,40,46,48,50,52,54,56, %T A207005 57,58,65,74,76,77,82,87,88,93,94,95,96,98,100,105,106,108,117,118, %U A207005 119,124,128,135,136,143,144,145,146,147,148,155,160,161,162,164 %N A207005 Numbers k such that omega(k) = omega(k - omega(k)) where omega(k) is the number of distinct primes dividing k. %C A207005 omega is the function in A001221. If there are infinitely many primes p such that p and 2p-1 are primes (see A005382), then this sequence is infinite. Proof: the numbers of the form 4p are in a subsequence if p and 2p-1 are both prime, because from the property that omega(4p) = 2 and omega(p(2p-1)) = 2, if n = 4p then omega(n-omega(n)) = omega(4p - 2) = omega(2(2p-1)) = 2 = omega(n). %H A207005 G. C. Greubel, <a href="/A207005/b207005.txt">Table of n, a(n) for n = 1..5000</a> %e A207005 12 is in the sequence because omega(12) = 2, omega(12 - 2) = omega(10) = 2. %t A207005 Select[Range[10^4],PrimeNu[#]==PrimeNu[#-PrimeNu[#]]&] %Y A207005 Cf. A001221, A005382. %K A207005 nonn %O A207005 1,2 %A A207005 _Michel Lagneau_, Feb 14 2012