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 A342051 #19 Apr 26 2021 21:28:39
%S A342051 1,3,5,6,7,9,11,12,13,15,17,18,19,21,23,24,25,27,29,31,33,35,36,37,39,
%T A342051 41,42,43,45,47,48,49,51,53,54,55,57,59,61,63,65,66,67,69,71,72,73,75,
%U A342051 77,78,79,81,83,84,85,87,89,91,93,95,96,97,99,101,102,103
%N A342051 Numbers k which have an even number of trailing zeros in their primorial base representation A049345(k).
%C A342051 Numbers k such that A276084(k) is even.
%C A342051 The number of terms not exceeding A002110(m) for m>=1 is A002110(m) * (1 - Sum_{k=1..m}(-1)^k/A002110(k)) = 1, 4, 19, 134, 1473, 19150, 325549 ...
%C A342051 The asymptotic density of this sequence is Sum_{k>=0} (-1)^k/A002110(k) = 0.637693... = 1 - A132120.
%C A342051 Also Heinz numbers of partitions with odd least gap. The least gap (mex or minimal excludant) of a partition is the least positive integer that is not a part. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions. - _Gus Wiseman_, Apr 23 2021
%H A342051 Amiram Eldar, <a href="/A342051/b342051.txt">Table of n, a(n) for n = 1..10000</a>
%H A342051 George E. Andrews and David Newman, <a href="https://doi.org/10.1007/s00026-019-00427-w">Partitions and the Minimal Excludant</a>, Annals of Combinatorics, Volume 23, May 2019, Pages 249-254.
%H A342051 Brian Hopkins, James A. Sellers, and Dennis Stanton, <a href="https://arxiv.org/abs/2009.10873">Dyson's Crank and the Mex of Integer Partitions</a>, arXiv:2009.10873 [math.CO], 2020.
%H A342051 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mex_(mathematics)">Mex (mathematics)</a>
%e A342051 1 is a term since A049345(1) = 1 has 0 trailing zero.
%e A342051 6 is a term since A049345(6) = 100 has 2 trailing zeros.
%e A342051 From _Gus Wiseman_, Apr 23 2021: (Start)
%e A342051 The sequence of terms together with their prime indices begins:
%e A342051 1: {} 25: {3,3} 51: {2,7}
%e A342051 3: {2} 27: {2,2,2} 53: {16}
%e A342051 5: {3} 29: {10} 54: {1,2,2,2}
%e A342051 6: {1,2} 31: {11} 55: {3,5}
%e A342051 7: {4} 33: {2,5} 57: {2,8}
%e A342051 9: {2,2} 35: {3,4} 59: {17}
%e A342051 11: {5} 36: {1,1,2,2} 61: {18}
%e A342051 12: {1,1,2} 37: {12} 63: {2,2,4}
%e A342051 13: {6} 39: {2,6} 65: {3,6}
%e A342051 15: {2,3} 41: {13} 66: {1,2,5}
%e A342051 17: {7} 42: {1,2,4} 67: {19}
%e A342051 18: {1,2,2} 43: {14} 69: {2,9}
%e A342051 19: {8} 45: {2,2,3} 71: {20}
%e A342051 21: {2,4} 47: {15} 72: {1,1,1,2,2}
%e A342051 23: {9} 48: {1,1,1,1,2} 73: {21}
%e A342051 24: {1,1,1,2} 49: {4,4} 75: {2,3,3}
%e A342051 (End)
%t A342051 seq[max_] := Module[{bases = Prime@Range[max, 1, -1], nmax}, nmax = Times @@ bases - 1; Select[Range[nmax], EvenQ @ LengthWhile[Reverse @ IntegerDigits[#, MixedRadix[bases]], #1 == 0 &] &]]; seq[4]
%t A342051 Select[Range[100],OddQ[Min@@Complement[Range[PrimeNu[#]+1],PrimePi/@First/@FactorInteger[#]]]&] (* _Gus Wiseman_, Apr 23 2021 *)
%Y A342051 Cf. A002110, A049345, A132120, A276084.
%Y A342051 Complement of A342050.
%Y A342051 A099788 is subsequence.
%Y A342051 Analogous sequences: A000201 (Zeckendorf representation), A003159 (binary), A007417 (ternary), A232744 (factorial base).
%Y A342051 The version for reversed binary expansion is A121539.
%Y A342051 Positions of odd terms in A257993.
%Y A342051 A000070 counts partitions with a selected part.
%Y A342051 A056239 adds up prime indices, row sums of A112798.
%Y A342051 A073491 lists numbers with gap-free prime indices.
%Y A342051 A079067 counts gaps in prime indices.
%Y A342051 A238709 counts partitions by sum and least difference.
%Y A342051 A339662 gives greatest gap in prime indices.
%Y A342051 Cf. A001223, A005408, A026794, A029707, A047235, A079068, A079523, A286469, A286470, A325351.
%K A342051 nonn,base
%O A342051 1,2
%A A342051 _Amiram Eldar_, Feb 26 2021