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A110473 Integers not in "array with primes".

%I A110473 #14 Jun 15 2021 11:04:32
%S A110473 1,9,15,18,21,25,27,30,33,35,36,39,42,45,49,50,51,54,55,57,60,63,65,
%T A110473 66,69,70,72,75,77,78,81,84,85,87,90,91,93,95,98,99,100,102,105,108,
%U A110473 110,111,114,115,117,119,120,121,123,125,126,129,130,132,133,135,138,140
%N A110473 Integers not in "array with primes".
%C A110473 This is 1 + A105441.
%e A110473 "Array with primes":
%e A110473 consider this array where the first column is made of all prime numbers p and the n-th term of a row is two times the previous one on the same row [p(n)=p*2^n]:
%e A110473 p p*2 p*4 p*8 p*16 p*32 p*64 p*128 p*256 p*512 ...
%e A110473 2 4 8 16 32 64 128 256 512 1024 ...
%e A110473 3 6 12 24 48 96 192 384 768 1536 ...
%e A110473 5 10 20 40 80 160 320 640 1280 2560 ...
%e A110473 7 14 28 56 112 224 448 896 1792 3584 ...
%e A110473 11 22 44 88 176 352 704 1408 2816 5632 ...
%e A110473 13 26 52 104 208 416 832 1664 3328 6656 ...
%e A110473 17 34 68 136 272 544 1088 2176 4352 8704 ...
%e A110473 19 38 76 152 304 608 1216 2432 4864 9728 ...
%e A110473 23 46 92 184 368 736 1472 2944 5888 11776 ...
%e A110473 29 58 116 232 464 928 1856 3712 7424 14848 ...
%e A110473 31 62 124 248 496 992 1984 3968 7936 15872 ...
%e A110473 37 74 148 296 592 1184 2368 4736 9472 18944 ...
%e A110473 41 82 164 328 656 1312 2624 5248 10496 20992 ...
%e A110473 43 86 172 344 688 1376 2752 5504 11008 22016 ...
%e A110473 47 94 188 376 752 1504 3008 6016 12032 24064 ...
%e A110473 53 106 212 424 848 1696 3392 6784 13568 27136 ...
%e A110473 ...
%p A110473 # The function tries to represent the idea; an
%p A110473 # implementation via A105441 would be more efficient.
%p A110473 A110473 := proc(n) local T;
%p A110473 T := proc(n) local A,i,l,h,k; A := [];
%p A110473 k := simplify(floor(log[2](n+1))-1);
%p A110473 for i from 0 to k do
%p A110473     l := iquo(n,2^(i+1))+1; h := iquo(n,2^i);
%p A110473     A := [op(A), select(isprime, [$l..h])] od;
%p A110473 convert(A,set) end;
%p A110473 `if`(T(n-1) minus T(n) = {}, n, NULL) end:
%p A110473 seq(A110473(i),i=1..140); # _Peter Luschny_, Mar 18 2013
%t A110473 With[{nn=150},Complement[Range[nn],Sort[Flatten[Table[Prime[n]*2^Range[ 0,nn],{n,nn}]]]]] (* _Harvey P. Dale_, Oct 18 2013 *)
%K A110473 easy,nonn
%O A110473 1,2
%A A110473 _Eric Angelini_ and _Alexandre Wajnberg_, Sep 08 2005