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 A260872 #25 Jun 09 2022 19:37:33
%S A260872 1,33,57,73,105,129,145,177,193,201,217,249,273,313,337,345,385,393,
%T A260872 409,457,465,481,537,553,561,577,609,633,649,673,697,705,745,753,777,
%U A260872 793,817,849,865,889,897,913,921,969,985,1009,1041,1065,1081,1113,1129
%N A260872 Squarefree numbers k such that k+1 has no primes of the form 4*m-1 and at most one 2 in its prime factorization.
%C A260872 An even number k is congruent to either 0 or 2 mod 4. If congruent to 0, it is divisible by 4 and thus not squarefree. If k is congruent to 2, k+1 will be one less than a multiple of 4, and thus at least one prime factor of k+1 will be one less than a multiple of 4. Thus, there are no even numbers in this sequence.
%C A260872 From the author's comment above, all sequence terms must be odd, so k+1 must always be even and k+1 will always be singly even. - _Ray Chandler_, Aug 03 2015
%H A260872 Amiram Eldar, <a href="/A260872/b260872.txt">Table of n, a(n) for n = 1..10000</a>
%e A260872 41 + 1 = 42 = 2*3*7 and both 3 and 7 are prime numbers of the form 4*n-1, so 41 is not a term of this sequence.
%t A260872 Select[Range[1100],SquareFreeQ[#]&&IntegerExponent[#+1,2]<2&&Select[First/@FactorInteger[#+1],Mod[#,4]==3&]=={}&] (* _Ray Chandler_, Aug 02 2015 *)
%Y A260872 Cf. A002144, A002145, A004613, A004614, A005117, A016825.
%K A260872 nonn
%O A260872 1,2
%A A260872 _J. Lowell_, Aug 01 2015