A384875 Irregular triangle T(n,k) = 2^(floor(n/3)-k) * nextprime(2^(n-2*(floor(n/3)-k))), with k = 0..floor(n/3)-1.

6, 10, 22, 20, 34, 44, 74, 68, 134, 88, 148, 262, 136, 268, 514, 296, 524, 1042, 272, 536, 1028, 2062, 592, 1048, 2084, 4106, 1072, 2056, 4124, 8198, 1184, 2096, 4168, 8212, 16418, 2144, 4112, 8248, 16396, 32822, 4192, 8336, 16424, 32836, 65542, 4288, 8224, 16496, 32792, 65644, 131074

Offset

3,1

Links

Michael De Vlieger, Table of n, a(n) for n = 3..10377 (rows n = 3..250, flattened).

Michael De Vlieger, Log log scatterplot showing the first 2380 terms.

Formula

A010846(T(n,k)) = n+2.

Example

Table begins:
  n\k     0      1      2      3       4
 ---------------------------------------
  3:      6
  4:     10
  5:     22
  6:     20     34
  7:     44     74
  8:     68    134
  9:     88    148    262
 10:    136    268    514
 11:    296    524   1042
 12:    272    536   1028   2062
 13:    592   1048   2084   4106
 14:   1072   2056   4124   8198
 15:   1184   2096   4168   8212   16418
 ...
Let S = A010846.
Tables showing terms in row a(n) of A162306, listed in order of row a(n) of A275280.
T(3,1) = 6,
S(6) = 5:
 1  2  4
 3  6
T(4,1) = 10,
S(10) = 6:
 1  2  4  8
 5 10
T(5,1) = 22,
S(22) = 7:
 1  2  4  8  16
11 22
T(6,1) = 20,               T(6,2) = 34,
S(20) = 8:                 S(34) = 8:
 1  2  4  8  16             1  2  4  8  16  32
 5 10 20                   17 34
T(7,1) = 44,               T(7,2) = 74,
S(44) = 9:                 S(74) = 9:
 1  2  4  8  16  32         1  2  4  8  16  32  64
11 22 44                   37 74
T(8,1) = 68,               T(8,2) = 134,
S(68) = 10:                S(134) = 10:
 1  2  4  8  16  32  64     1  2  4  8  ...  128
17 34 68                   67 134
T(9,1) = 88,               T(9,2) = 148,            T(9,3) = 262,
S(88) = 11:                S(148) = 11:             S(262) = 11:
 1  2  4  8  16  32  64     1  2  4  8  ...  128      1   2  ... 256
11 22 44 88                37 74 148                131 262
etc.

Mathematica

Table[2^k*NextPrime[2^(n - 2*k)], {n, 3, 18}, {k, Floor[n/3], 1, -1}] // TableForm

Crossrefs

Cf. A006881, A010846, A100484.

Sequence in context: A287993 A220035 A083285 * A082419 A102783 A369656

Adjacent sequences: A384872 A384873 A384874 * A384876 A384877 A384878

Keyword

nonn,tabf,easy

Author

Michael De Vlieger, Jun 11 2025

Status

approved