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 A269345 #41 Feb 16 2025 08:33:30 %S A269345 25,33,49,55,63,75,85,91,93,115,117,119,121,123,133,141,143,145,153, %T A269345 159,169,175,183,185,187,201,203,205,207,213,215,217,219,235,243,245, %U A269345 247,253,259,265,273,285,287,289,295,297,299,301,303,319,321,323,325,327,333 %N A269345 Smaller of two consecutive odd numbers that are composites. %C A269345 Analogous to A001359 for odd composite numbers (A071904). %C A269345 Consists of numbers that cannot be the difference of two primes: an odd number m can be the difference of two primes only if m+2 is prime, which cannot be the case for any a(n) as a(n)+2 is composite. %C A269345 Some terms form subsequences of perfect powers, e.g., A106564 (for squares) and A269346 (for cubes). %C A269345 Any composite of the form 6k+1 (A016921) is a term: (6k+1)+2 = 3(2k+1) is both odd and composite as a product of two odd numbers, thus 6k+1, being odd, is a term if it is composite. %H A269345 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinComposites.html">Twin Composites</a> %F A269345 a(n) = A061673(n) - 1. - _M. F. Hasler_, Nov 18 2018 %e A269345 25 belongs to this sequence because 27=25+2 is the next odd composite. %t A269345 Select[Range[450], OddQ[#]&& !PrimeQ[#]&&!PrimeQ[#+2]&] %o A269345 (PARI) for(n=1, 450, n%2==1&&!isprime(n)&&!isprime(n+2)&&print1(n, ", ")) %o A269345 (Magma) [n: n in [1..350]| not IsPrime(n) and not IsPrime(n+2) and n mod 2 eq 1]; // _Vincenzo Librandi_, Feb 28 2016 %Y A269345 Cf. A071904 (odd composites), A001359 (similar sequence for primes). %Y A269345 Cf. A106564, A269346. %Y A269345 Cf. A061673. %K A269345 nonn %O A269345 1,1 %A A269345 _Waldemar Puszkarz_, Feb 24 2016 %E A269345 Name edited by _Michel Marcus_, Jul 27 2023