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A295642 Lexicographically earliest sequence of distinct prime numbers such that, for any n > 0, a(n) AND n = n (where AND denotes the binary AND operator).

%I A295642 #12 Nov 28 2017 11:55:45
%S A295642 3,2,7,5,13,23,31,11,29,43,47,61,79,127,191,17,19,59,83,53,149,151,
%T A295642 223,89,157,251,283,317,349,383,479,37,41,103,107,101,109,167,239,173,
%U A295642 233,367,379,431,509,751,1087,113,179,307,311,181,373,439,503,313,443
%N A295642 Lexicographically earliest sequence of distinct prime numbers such that, for any n > 0, a(n) AND n = n (where AND denotes the binary AND operator).
%C A295642 This sequence is a permutation of the prime numbers (A000040) and for any prime p, a(n) = p for some n <= p.
%C A295642 For any n > 0, a(n) >= A295609(n).
%H A295642 Rémy Sigrist, <a href="/A295642/b295642.txt">Table of n, a(n) for n = 1..10000</a>
%H A295642 Rémy Sigrist, <a href="/A295642/a295642.png">Scatterplot of the first 2^17 terms</a>
%H A295642 Rémy Sigrist, <a href="/A295642/a295642_1.png">Colored scatterplot of the first 2^17 terms</a> (where the color is function of A000120(n), the Hamming weight of n)
%H A295642 Rémy Sigrist, <a href="/A295642/a295642.txt">C++ program for A295642</a>
%e A295642 The first terms, alongside the binary representation of n and a(n), are:
%e A295642   n   a(n)   bin(n)  bin(a(n))
%e A295642   --  ----   ------  ---------
%e A295642    1     3        1         11
%e A295642    2     2       10         10
%e A295642    3     7       11        111
%e A295642    4     5      100        101
%e A295642    5    13      101       1101
%e A295642    6    23      110      10111
%e A295642    7    31      111      11111
%e A295642    8    11     1000       1011
%e A295642    9    29     1001      11101
%e A295642   10    43     1010     101011
%e A295642   11    47     1011     101111
%e A295642   12    61     1100     111101
%e A295642   13    79     1101    1001111
%e A295642   14   127     1110    1111111
%e A295642   15   191     1111   10111111
%e A295642   16    17    10000      10001
%e A295642   17    19    10001      10011
%e A295642   18    59    10010     111011
%e A295642   19    83    10011    1010011
%e A295642   20    53    10100     110101
%t A295642 Fold[Append[#1, Block[{p = 2}, While[Nand[FreeQ[#1, p], BitAnd[p, #2] == #2], p = NextPrime@ p]; p]] &, {3}, Range[2, 57]] (* _Michael De Vlieger_, Nov 26 2017 *)
%o A295642 (C++) See Links section.
%Y A295642 Cf. A000040, A000120, A295609.
%K A295642 nonn,base
%O A295642 1,1
%A A295642 _Rémy Sigrist_, Nov 25 2017