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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). 1
 3, 2, 7, 5, 13, 23, 31, 11, 29, 43, 47, 61, 79, 127, 191, 17, 19, 59, 83, 53, 149, 151, 223, 89, 157, 251, 283, 317, 349, 383, 479, 37, 41, 103, 107, 101, 109, 167, 239, 173, 233, 367, 379, 431, 509, 751, 1087, 113, 179, 307, 311, 181, 373, 439, 503, 313, 443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a permutation of the prime numbers (A000040) and for any prime p, a(n) = p for some n <= p. For any n > 0, a(n) >= A295609(n). LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, Scatterplot of the first 2^17 terms Rémy Sigrist, Colored scatterplot of the first 2^17 terms (where the color is function of A000120(n), the Hamming weight of n) Rémy Sigrist, C++ program for A295642 EXAMPLE The first terms, alongside the binary representation of n and a(n), are:   n   a(n)   bin(n)  bin(a(n))   --  ----   ------  ---------    1     3        1         11    2     2       10         10    3     7       11        111    4     5      100        101    5    13      101       1101    6    23      110      10111    7    31      111      11111    8    11     1000       1011    9    29     1001      11101   10    43     1010     101011   11    47     1011     101111   12    61     1100     111101   13    79     1101    1001111   14   127     1110    1111111   15   191     1111   10111111   16    17    10000      10001   17    19    10001      10011   18    59    10010     111011   19    83    10011    1010011   20    53    10100     110101 MATHEMATICA 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 *) PROG (C++) See Links section. CROSSREFS Cf. A000040, A000120, A295609. Sequence in context: A006921 A292204 A292203 * A014693 A318783 A253564 Adjacent sequences:  A295639 A295640 A295641 * A295643 A295644 A295645 KEYWORD nonn,base AUTHOR Rémy Sigrist, Nov 25 2017 STATUS approved

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Last modified June 24 23:57 EDT 2021. Contains 345445 sequences. (Running on oeis4.)