cp's OEIS Frontend

A372438 Least binary index equals greatest prime index.

%I A372438 #6 May 05 2024 10:42:14
%S A372438 6,18,20,54,56,60,100,162,168,176,180,280,300,392,416,486,500,504,528,
%T A372438 540,840,880,900,1088,1176,1232,1248,1400,1458,1500,1512,1584,1620,
%U A372438 1936,1960,2080,2432,2500,2520,2640,2700,2744,2912,3264,3528,3696,3744,4200
%N A372438 Least binary index equals greatest prime index.
%C A372438 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
%C A372438 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A372438 Are there any squarefree terms > 6?
%F A372438 A001511(a(n)) = A061395(a(n)).
%e A372438 The binary indices of 60 are {3,4,5,6}, the prime indices are {1,1,2,3}, and 3 = 3, so 60 is in the sequence.
%e A372438 The terms together with their prime indices begin:
%e A372438      6: {1,2}
%e A372438     18: {1,2,2}
%e A372438     20: {1,1,3}
%e A372438     54: {1,2,2,2}
%e A372438     56: {1,1,1,4}
%e A372438     60: {1,1,2,3}
%e A372438    100: {1,1,3,3}
%e A372438    162: {1,2,2,2,2}
%e A372438    168: {1,1,1,2,4}
%e A372438    176: {1,1,1,1,5}
%e A372438    180: {1,1,2,2,3}
%e A372438    280: {1,1,1,3,4}
%e A372438    300: {1,1,2,3,3}
%e A372438 The terms together with their binary expansions and binary indices begin:
%e A372438      6:            110 ~ {2,3}
%e A372438     18:          10010 ~ {2,5}
%e A372438     20:          10100 ~ {3,5}
%e A372438     54:         110110 ~ {2,3,5,6}
%e A372438     56:         111000 ~ {4,5,6}
%e A372438     60:         111100 ~ {3,4,5,6}
%e A372438    100:        1100100 ~ {3,6,7}
%e A372438    162:       10100010 ~ {2,6,8}
%e A372438    168:       10101000 ~ {4,6,8}
%e A372438    176:       10110000 ~ {5,6,8}
%e A372438    180:       10110100 ~ {3,5,6,8}
%e A372438    280:      100011000 ~ {4,5,9}
%e A372438    300:      100101100 ~ {3,4,6,9}
%t A372438 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372438 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372438 Select[Range[1000],Min[bix[#]]==Max[prix[#]]&]
%Y A372438 Same length: A071814, zeros of A372441.
%Y A372438 Same sum: A372427, zeros of A372428.
%Y A372438 Same maxima: A372436, zeros of A372442.
%Y A372438 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372438 A029837 gives greatest binary index, least A001511.
%Y A372438 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372438 A061395 gives greatest prime index, least A055396.
%Y A372438 A070939 gives length of binary expansion.
%Y A372438 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372438 Cf. A000720, A014499, A030101, A061712, A318283, A355536, A359401, A359402, A372429-A372433.
%K A372438 nonn,base
%O A372438 1,1
%A A372438 _Gus Wiseman_, May 04 2024