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 A141465 #14 Jan 25 2023 09:16:08 %S A141465 2,3,2,5,3,11,17,29,41,59,71,101,107,137,149,179,191,197,227,239,269, %T A141465 281,311,347,419,431,461,521,569,599,617,641,659,809,821,827,857,881, %U A141465 1019,1031,1049,1061,1091,1151,1229,1277,1289,1301,1319,1427,1451,1481 %N A141465 Prime transformed products of prime factors of the composites, the largest prime decremented by 2, the smallest by 1. %C A141465 In the prime factorization of k=A002808(i), i=1,2,3,..., one instance of the largest prime, pmax=A052369(i), is replaced by pmax-2 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin-1. If the product of this modified set of factors, k*(pmax-2)*(pmin-1)/(pmin*pmax), is prime, it is appended to the sequence. %e A141465 composite k transformed product %e A141465 ----------- ------------------------- %e A141465 4 = 2*2 (2-1)*(2-2) = 1*0 = 0 (nonprime) %e A141465 6 = 2*3 (2-1)*(3-2) = 1*1 = 1 (nonprime) %e A141465 8 = 2*2*2 (2-1)*2*(2-2) = 1*2*0 = 0 (nonprime) %e A141465 9 = 3*3 (3-1)*(3-2) = 2*1 = 2 = a(1) %e A141465 10 = 2*5 (2-1)*(5-2) = 1*3 = 3 = a(2) %e A141465 12 = 2*2*3 (2-1)*2*(3-2) = 1*2*1 = 2 = a(3) %e A141465 14 = 2*7 (2-1)*(7-2) = 1*5 = 5 = a(4) %K A141465 nonn %O A141465 1,1 %A A141465 _Juri-Stepan Gerasimov_, Aug 08 2008 %E A141465 Edited by _Jon E. Schoenfield_, Feb 20 2021