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 A376839 #11 Nov 01 2024 23:54:45
%S A376839 1,2,3,4,5,6,7,8,11,10,9,12,13,14,15,16,17,18,19,20,21,22,24,23,26,27,
%T A376839 28,30,29,32,31,34,33,36,37,38,39,40,42,25,44,45,46,48,41,50,51,52,54,
%U A376839 43,56,57,58,60,47,62,63,64,53,66,35,68,69,70,72,59,74,75
%N A376839 a(1) = 1. For n > 1 if A007947(a(n-1)) is in A002110, a(n) is the smallest prime not already a term. Otherwise a(n) is the least novel multiple of the smallest non divisor prime of a(n-1).
%C A376839 A non divisor prime of a(n-1) is any prime p < Gpf(a(n-1)) which does not divide a(n-1). A007947(a(n-1)) is in A002110 iff a(n-1) is a term in A055932. Sequence is conjectured to be a permutation of the natural numbers (A000027) with primes in order.
%C A376839 Scatterplot shows trajectories of numbers whose smallest prime factor is prime p, e.g., for p = 5, numbers in A084967, p = 7, those in A084968, p = 11 those in A084969, etc. - _Michael De Vlieger_, Oct 09 2024
%H A376839 Michael De Vlieger, <a href="/A376839/b376839.txt">Table of n, a(n) for n = 1..10000</a>
%H A376839 Michael De Vlieger, <a href="/A376839/a376839.png">Log log scatterplot of a(n)</a>, n = 1..2^20.
%H A376839 Michael De Vlieger, <a href="/A376839/a376839_1.png">Log log scatterplot of a(n)</a>, n = 1..2^14, showing primes in red, perfect prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue or purple, with the latter additionally representing powerful numbers that are not prime powers.
%e A376839 a(1) = 1 = A002110(0) so a(2) = 2 (smallest prime not already a term).
%e A376839 a(2) = 2 = A002110(1) so a(3) = 3.
%e A376839 a(3) = 3 not a term in A002110 so a(4) is least novel multiple of 2, the least non divisor prime of 3. Therefore a(4) = 4 since 2 has occurred earlier.
%e A376839 a(39) = 42, not a term in A002110 so a(40) = 25, the least novel multiple of 5, the smallest non divisor prime of 42.
%t A376839 nn = 120; c[_] := False; m[_] := 1; f[x_] := FactorInteger[x][[All, 1]];
%t A376839 Array[Set[{a[#], c[#], m[#]}, {#, True, 2}] &, 2]; j = 2; v = 3;
%t A376839 Do[If[Or[IntegerQ@ Log2[j], And[EvenQ[j], Union@ Differences@ PrimePi[#] == {1}]],
%t A376839 k = v; While[c[k*m[k]], m[k]++]; k *= m[k],
%t A376839 k = 2; While[Divisible[j, k], k = NextPrime[k]];
%t A376839 While[c[k*m[k]], m[k]++]; k *= m[k]] &[f[j]];
%t A376839 Set[{a[n], c[k], j}, {k, True, k}];
%t A376839 If[k == v, While[c[v], v = NextPrime[v]]], {n, 3, nn}];
%t A376839 Array[a, nn] (* _Michael De Vlieger_, Oct 09 2024 *)
%Y A376839 Cf. A000040, A000027, A002110, A007947, A055932, A084967, A084968, A084969, A372368, A376865.
%K A376839 nonn
%O A376839 1,2
%A A376839 _David James Sycamore_, Oct 06 2024
%E A376839 More terms from _Michael De Vlieger_, Oct 09 2024