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 A111107 #31 Jun 06 2025 18:17:41
%S A111107 2,3,5,11,13,29,43,53,59,71,79,83,103,113,139,173,181,227,269,277,317,
%T A111107 383,463,509,673,701,751,863,967,977,1187,1201,1493,1531,1609,1637,
%U A111107 1801,2153,2221,2239,2371,2377,2543,2557,2683,2687,2791,2837,3067,3229,3257
%N A111107 Lexicographically smallest increasing sequence of primes whose binomial transform consists only of primes.
%C A111107 In the standard binomial transform of the primes most of the terms are composite.
%H A111107 Alois P. Heinz, <a href="/A111107/b111107.txt">Table of n, a(n) for n = 0..2000</a>
%F A111107 a(n) = Sum_{i=0..n} A384676(n-i)*binomial(n,i)*(-1)^i. - _Alois P. Heinz_, Jun 06 2025
%e A111107 The binomial transform of this sequence gives: 2, 5, 13, 37, 101, 271, 727, 1931, 5003, 12547, 30449, 71761, ... = A384676.
%e A111107 The prime 7 and various larger primes are missing from the new sequence because the transform would not consist of primes. For example,
%e A111107 2,5,13,33
%e A111107 3,8,20
%e A111107 5,12
%e A111107 7
%e A111107 and 33 is not prime, so we must eliminate 7.
%Y A111107 Cf. A000040, A007443, A384676.
%K A111107 easy,nonn
%O A111107 0,1
%A A111107 _Daniel Joyce_, Oct 14 2005
%E A111107 Offset set to 0 by _Alois P. Heinz_, Jun 06 2025