A110473 Integers not in "array with primes".

1, 9, 15, 18, 21, 25, 27, 30, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 125, 126, 129, 130, 132, 133, 135, 138, 140

Offset

1,2

Comments

This is 1 + A105441.

Links

Table of n, a(n) for n=1..62.

Example

"Array with primes":
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]:
p p*2 p*4 p*8 p*16 p*32 p*64 p*128 p*256 p*512 ...
2 4 8 16 32 64 128 256 512 1024 ...
3 6 12 24 48 96 192 384 768 1536 ...
5 10 20 40 80 160 320 640 1280 2560 ...
7 14 28 56 112 224 448 896 1792 3584 ...
11 22 44 88 176 352 704 1408 2816 5632 ...
13 26 52 104 208 416 832 1664 3328 6656 ...
17 34 68 136 272 544 1088 2176 4352 8704 ...
19 38 76 152 304 608 1216 2432 4864 9728 ...
23 46 92 184 368 736 1472 2944 5888 11776 ...
29 58 116 232 464 928 1856 3712 7424 14848 ...
31 62 124 248 496 992 1984 3968 7936 15872 ...
37 74 148 296 592 1184 2368 4736 9472 18944 ...
41 82 164 328 656 1312 2624 5248 10496 20992 ...
43 86 172 344 688 1376 2752 5504 11008 22016 ...
47 94 188 376 752 1504 3008 6016 12032 24064 ...
53 106 212 424 848 1696 3392 6784 13568 27136 ...
...

Maple

# The function tries to represent the idea; an
# implementation via A105441 would be more efficient.
A110473 := proc(n) local T;
T := proc(n) local A, i, l, h, k; A := [];
k := simplify(floor(log[2](n+1))-1);
for i from 0 to k do
    l := iquo(n, 2^(i+1))+1; h := iquo(n, 2^i);
    A := [op(A), select(isprime, [$l..h])] od;
convert(A, set) end;
`if`(T(n-1) minus T(n) = {}, n, NULL) end:
seq(A110473(i), i=1..140); # Peter Luschny, Mar 18 2013

Mathematica

With[{nn=150}, Complement[Range[nn], Sort[Flatten[Table[Prime[n]*2^Range[ 0, nn], {n, nn}]]]]] (* Harvey P. Dale, Oct 18 2013 *)

Crossrefs

Sequence in context: A316752 A358725 A358576 * A105441 A325164 A093642

Adjacent sequences: A110470 A110471 A110472 * A110474 A110475 A110476

Keyword

easy,nonn

Author

Eric Angelini and Alexandre Wajnberg, Sep 08 2005

Status

approved