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 A072592 #12 Jul 07 2024 13:44:50 %S A072592 10,20,26,30,34,40,50,52,58,60,68,70,74,78,80,82,90,100,102,104,106, %T A072592 110,116,120,122,130,136,140,146,148,150,156,160,164,170,174,178,180, %U A072592 182,190,194,200,202,204,208,210,212,218,220,222,226,230,232,234,238 %N A072592 Even numbers with at least one prime factor of form 4*k+1. %C A072592 Conjecture: this is exactly the sequence whose terms are twice those of A009003. (This has been verified for all terms<=500.) Compare A009003. - _John W. Layman_, Mar 12 2008 %C A072592 The conjecture is true. See comments on A008846 and A004613. - Lambert Herrgesell (zero815(AT)googlemail.com), Apr 24 2008 %H A072592 Harvey P. Dale, <a href="/A072592/b072592.txt">Table of n, a(n) for n = 1..1000</a> %F A072592 A072591(a(n)) = 0. %t A072592 opfQ[n_]:=Count[Transpose[FactorInteger[n]][[1]],_?(IntegerQ[ (#-1)/4]&)]>0; Select[Range[2,250,2],opfQ] (* _Harvey P. Dale_, Jun 02 2012 *) %o A072592 (Python) %o A072592 from itertools import count, islice %o A072592 from sympy import primefactors %o A072592 def A072592_gen(startvalue=1): # generator of terms >= startvalue %o A072592 return (n<<1 for n in count(max(startvalue,1)) if any(p&3==1 for p in primefactors(n))) %o A072592 A072592_list = list(islice(A072592_gen(),20)) # _Chai Wah Wu_, Jul 07 2024 %Y A072592 Cf. A005843, A002144, A072591, A009003, A008846, A004613. %K A072592 nonn %O A072592 1,1 %A A072592 _Reinhard Zumkeller_, Jun 23 2002