A289171 Irregular triangle T(n, k) read by rows with 1 <= k <= n: T(n, 1) = A020900(n - k + 1) - (n - k + 1) and T(n, k) = max(0, T(n - 1, k - 1) - 1) otherwise.

1, 1, 1, 2, 3, 1, 3, 2, 4, 2, 1, 4, 3, 1, 5, 3, 2, 6, 4, 2, 1, 7, 5, 3, 1, 9, 6, 4, 2, 9, 8, 5, 3, 1, 9, 8, 7, 4, 2, 9, 8, 7, 6, 3, 1, 11, 8, 7, 6, 5, 2, 13, 10, 7, 6, 5, 4, 1, 12, 12, 9, 6, 5, 4, 3, 13, 11, 11, 8, 5, 4, 3, 2, 14, 12, 10, 10, 7, 4, 3, 2, 1

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..13692 (rows 1 <= n <= 250).

Formula

Row lengths = A107347(n + 1).

Example

Triangle begins:
n  a(n)
1:    0
2:    1
3:    1
4:    2
5:    3   1
6:    3   2
7:    4   2   1
8:    4   3   1
9:    5   3   2
10:   6   4   2   1
11:   7   5   3   1
12:   9   6   4   2
13:   9   8   5   3   1
14:   9   8   7   4   2
15:   9   8   7   6   3   1
16:  11   8   7   6   5   2
17:  13  10   7   6   5   4   1
18:  12  12   9   6   5   4   3
19:  13  11  11   8   5   4   3   2
20:  14  12  10  10   7   4   3   2   1
   ...

Mathematica

T[n_, k_] := T[n, k] = If[k == 1, PrimePi[2 Prime@ #] - # &[n - k + 1], Max[0, T[n - 1, k - 1] - 1]]; Map[DeleteCases[#, 0] &, Table[T[n, k], {n, 20}, {k, n}]] // Flatten (* or *)
T[n_, k_] := T[n, k] = If[k == 1, PrimePi[2 Prime@ #] - # &[n - k + 1], Max[0, T[n - 1, k - 1] - 1]]; Table[T[n, k], {n, 60}, {k, Count[Range[# + 1, 2 # - 1] &@ Prime[n + 1], s_ /; PrimeOmega@ s == 2 && EvenQ@ s]}] // Flatten (* Michael De Vlieger, Jul 21 2017 *)

Crossrefs

Cf. A001221, A002110, A006530, A020900, A053669, A107347, A288813.

Sequence in context: A107796 A194308 A257070 * A231633 A039702 A230294

Adjacent sequences: A289168 A289169 A289170 * A289172 A289173 A289174

Keyword

nonn,tabf,easy

Author

Michael De Vlieger, Jul 21 2017

Status

approved