cp's OEIS Frontend

A325097 Heinz numbers of integer partitions whose distinct parts have no binary carries.

%I A325097 #7 Jul 27 2019 14:57:51
%S A325097 1,2,3,4,5,6,7,8,9,11,12,13,14,16,17,18,19,21,23,24,25,26,27,28,29,31,
%T A325097 32,33,35,36,37,38,41,42,43,47,48,49,52,53,54,56,57,58,59,61,63,64,67,
%U A325097 69,71,72,73,74,76,79,81,83,84,86,89,95,96,97,98,99,101
%N A325097 Heinz numbers of integer partitions whose distinct parts have no binary carries.
%C A325097 A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
%C A325097 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose distinct prime indices have no binary carries.
%e A325097 Most small numbers are in the sequence, however the sequence of non-terms together with their prime indices begins:
%e A325097   10: {1,3}
%e A325097   15: {2,3}
%e A325097   20: {1,1,3}
%e A325097   22: {1,5}
%e A325097   30: {1,2,3}
%e A325097   34: {1,7}
%e A325097   39: {2,6}
%e A325097   40: {1,1,1,3}
%e A325097   44: {1,1,5}
%e A325097   45: {2,2,3}
%e A325097   46: {1,9}
%e A325097   50: {1,3,3}
%e A325097   51: {2,7}
%e A325097   55: {3,5}
%e A325097   60: {1,1,2,3}
%e A325097   62: {1,11}
%e A325097   65: {3,6}
%e A325097   66: {1,2,5}
%e A325097   68: {1,1,7}
%e A325097   70: {1,3,4}
%t A325097 binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A325097 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A325097 Select[Range[100],stableQ[PrimePi/@First/@FactorInteger[#],Intersection[binpos[#1],binpos[#2]]!={}&]&]
%Y A325097 Cf. A000110, A000720, A001222, A050315, A056239, A080572, A112798, A247935.
%Y A325097 Cf. A325094, A325095, A325096, A325097, A325098, A325100, A325102, A325103.
%K A325097 nonn
%O A325097 1,2
%A A325097 _Gus Wiseman_, Mar 27 2019