A369276 Numbers k in A126706 such that either k-1 or k+1 or both are also in A126706.

44, 45, 75, 76, 98, 99, 100, 116, 117, 135, 136, 147, 148, 152, 153, 171, 172, 175, 176, 188, 189, 207, 208, 224, 225, 244, 245, 260, 261, 275, 276, 279, 280, 296, 297, 315, 316, 324, 325, 332, 333, 350, 351, 352, 363, 364, 368, 369, 375, 376, 387, 388, 404, 405

Offset

1,1

Comments

A369954 is a proper subset.

Complement of A369516 relative to A126706.

Seen as a table where terms are consecutive, row n contains no primes; corollary: numbers in row n exceed prime(i) but are less than prime(i+1) for some i.

Smallest k such that row n has length m appear in A356322. Rows have length m > 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11053

Example

Seen as a table T(n,j), row n contains the following terms:
      n
      1:     44,     45;
      2:     75,     76;
      3:     98,     99,    100;
      4:    116,    117;
      5:    135,    136;
      6:    147,    148;
      7:    152,    153;
            ...
     59:    844,    845,    846,    847,    848;
            ...
    235:   2888,   2889,   2890,   2891,   2892;
            ...
    255:   3174,   3175,   3176,   3177;
            ...
    293:   3624,   3625,   3626,   3627,   3628;
            ...
   1898:  22020,  22021,  22022,  22023,  22024,  22025;
            ...
  19018: 217070, 217071, 217072, 217073, 217074, 217075, 217076;
            ...

Mathematica

Select[Select[Range[500], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], AnyTrue[{# - 1, # + 1}, Nor[SquareFreeQ[#], PrimePowerQ[#]] &] &]

Crossrefs

Cf. A126706, A356322, A369516, A369954.

Sequence in context: A112815 A354145 A242934 * A038400 A364657 A254750

Adjacent sequences: A369273 A369274 A369275 * A369277 A369278 A369279

Keyword

nonn,easy

Author

Michael De Vlieger, Mar 24 2024

Status

approved