cp's OEIS Frontend

A372436 Numbers whose binary indices and prime indices have the same maximum.

%I A372436 #6 May 05 2024 08:54:48
%S A372436 3,5,14,22,39,52,68,85,102,119,133,152,171,190,209,228,247,276,299,
%T A372436 322,345,368,391,414,437,460,483,506,522,551,580,609,638,667,696,725,
%U A372436 754,783,812,841,870,928,957,986,1015,1054,1085,1116,1178,1209,1240,1302
%N A372436 Numbers whose binary indices and prime indices have the same maximum.
%C A372436 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 A372436 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 A372436 Note that a number's binary and prime indices cannot have the same minimum; see A372437.
%F A372436 A070939(a(n)) = A061395(a(n)).
%e A372436 The binary indices of 345 are {1,4,5,7,9}, and the prime indices are {2,3,9}. Both have maximum 9, so 345 is in the sequence.
%e A372436 The terms together with their prime indices begin:
%e A372436      3: {2}
%e A372436      5: {3}
%e A372436     14: {1,4}
%e A372436     22: {1,5}
%e A372436     39: {2,6}
%e A372436     52: {1,1,6}
%e A372436     68: {1,1,7}
%e A372436     85: {3,7}
%e A372436    102: {1,2,7}
%e A372436    119: {4,7}
%e A372436    133: {4,8}
%e A372436    152: {1,1,1,8}
%e A372436    171: {2,2,8}
%e A372436 The terms together with their binary expansions and binary indices begin:
%e A372436      3:           11 ~ {1,2}
%e A372436      5:          101 ~ {1,3}
%e A372436     14:         1110 ~ {2,3,4}
%e A372436     22:        10110 ~ {2,3,5}
%e A372436     39:       100111 ~ {1,2,3,6}
%e A372436     52:       110100 ~ {3,5,6}
%e A372436     68:      1000100 ~ {3,7}
%e A372436     85:      1010101 ~ {1,3,5,7}
%e A372436    102:      1100110 ~ {2,3,6,7}
%e A372436    119:      1110111 ~ {1,2,3,5,6,7}
%e A372436    133:     10000101 ~ {1,3,8}
%e A372436    152:     10011000 ~ {4,5,8}
%e A372436    171:     10101011 ~ {1,2,4,6,8}
%t A372436 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372436 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372436 Select[Range[100],Max[prix[#]]==Max[bix[#]]&]
%Y A372436 For length instead of maximum we have A071814.
%Y A372436 For sum instead of maximum we have A372427.
%Y A372436 Positions of zeros in A372442, for minimum instead of maximum A372437.
%Y A372436 A003963 gives product of prime indices.
%Y A372436 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372436 A029837 gives greatest binary index, least A001511.
%Y A372436 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372436 A061395 gives greatest prime index, least A055396.
%Y A372436 A070939 gives length of binary expansion.
%Y A372436 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372436 Cf. A000720, A014499, A030101, A066099, A096111, A304818, A355536, A359401, A359402, A372428-A372433, A372441.
%K A372436 nonn,base
%O A372436 1,1
%A A372436 _Gus Wiseman_, May 04 2024