cp's OEIS Frontend

A372588 Numbers k > 1 such that (greatest binary index of k) + (greatest prime index of k) is odd.

%I A372588 #6 May 15 2024 16:28:59
%S A372588 2,6,7,8,10,11,15,18,19,21,24,26,27,28,29,32,33,34,40,41,44,45,46,47,
%T A372588 50,51,55,59,60,62,65,70,71,72,74,76,78,79,81,84,86,87,89,91,95,96,98,
%U A372588 101,104,105,106,107,108,111,112,113,114,116,117,122,126,128
%N A372588 Numbers k > 1 such that (greatest binary index of k) + (greatest prime index of k) is odd.
%C A372588 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 A372588 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 A372588 The even version is A372589.
%F A372588 Numbers k such that A070939(k) + A061395(k) is odd.
%e A372588 The terms (center), their binary indices (left), and their weakly decreasing prime indices (right) begin:
%e A372588         {2}   2  (1)
%e A372588       {2,3}   6  (2,1)
%e A372588     {1,2,3}   7  (4)
%e A372588         {4}   8  (1,1,1)
%e A372588       {2,4}  10  (3,1)
%e A372588     {1,2,4}  11  (5)
%e A372588   {1,2,3,4}  15  (3,2)
%e A372588       {2,5}  18  (2,2,1)
%e A372588     {1,2,5}  19  (8)
%e A372588     {1,3,5}  21  (4,2)
%e A372588       {4,5}  24  (2,1,1,1)
%e A372588     {2,4,5}  26  (6,1)
%e A372588   {1,2,4,5}  27  (2,2,2)
%e A372588     {3,4,5}  28  (4,1,1)
%e A372588   {1,3,4,5}  29  (10)
%e A372588         {6}  32  (1,1,1,1,1)
%e A372588       {1,6}  33  (5,2)
%e A372588       {2,6}  34  (7,1)
%e A372588       {4,6}  40  (3,1,1,1)
%e A372588     {1,4,6}  41  (13)
%e A372588     {3,4,6}  44  (5,1,1)
%e A372588   {1,3,4,6}  45  (3,2,2)
%t A372588 Select[Range[2,100],OddQ[IntegerLength[#,2]+PrimePi[FactorInteger[#][[-1,1]]]]&]
%Y A372588 For sum (A372428, zeros A372427) we have A372586.
%Y A372588 For minimum (A372437) we have A372439, complement A372440.
%Y A372588 For length (A372441, zeros A071814) we have A372590, complement A372591.
%Y A372588 Positions of odd terms in A372442, zeros A372436.
%Y A372588 The complement is A372589.
%Y A372588 For just binary indices:
%Y A372588 - length: A000069, complement A001969
%Y A372588 - sum: A158705, complement A158704
%Y A372588 - minimum: A003159, complement A036554
%Y A372588 - maximum: A053738, complement A053754
%Y A372588 For just prime indices:
%Y A372588 - length: A026424 (count A027193), complement A028260 (count A027187)
%Y A372588 - sum: A300063 (count A058695), complement A300061 (count A058696)
%Y A372588 - minimum: A340932 (count A026804), complement A340933 (count A026805)
%Y A372588 - maximum: A244991 (count A027193), complement A244990 (count A027187)
%Y A372588 A005408 lists odd numbers.
%Y A372588 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372588 A029837 gives greatest binary index, least A001511.
%Y A372588 A031368 lists odd-indexed primes, even A031215.
%Y A372588 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372588 A061395 gives greatest prime index, least A055396.
%Y A372588 A070939 gives length of binary expansion.
%Y A372588 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372588 Cf. A000720, A006141, A066208, A160786, A243055, A257991, A300272, A304818, A340604, A341446, A372429-A372433, A372438.
%K A372588 nonn
%O A372588 1,1
%A A372588 _Gus Wiseman_, May 14 2024