A298760 Numbers k such that there is a record number of consecutive prime centered k-gonal numbers after 1.

1, 2, 6, 10, 46, 102, 7186, 6382932

Offset

1,2

Comments

The number of consecutive primes is 1, 3, 4, 7, 8, 9, 10, 11.

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Wikipedia, Centered polygonal number

Example

The first 8 centered 10-gonal numbers (A062786) are 1, 11, 31, 61, 101, 151, 211, 281, and all of them except for 1 are primes (A090562). The previous record is 4 primes, for centered hexagonal numbers 7, 19, 37, 61 (A003215), therefore 6 and 10 are in the sequence.
From Michel Marcus, Feb 12 2018: (Start)
  Number of primes after the 1
1: 1  2  4  7  11  16 ...  : 1   <- record
2: 1  3  7 13  21  31 ...  : 3   <- record
3: 1  4 10 19  31  46 ...  : 0
4: 1  5 13 25  41  61 ...  : 2
5: 1  6 16 31  51  76 ...  : 0
6: 1  7 19 37  61  91 ...  : 4   <- record
....
(End)

Mathematica

f[n_, k_] := k*n (n - 1)/2 + 1; a[k_] := Module[{n = 2}, While[PrimeQ[f[n, k]], n++]; n - 2]; am = 0; seq={}; Do[a1 = a[n]; If[a1 > am, AppendTo[seq, n]; am = a1], {n, 1, 10^7}]; seq

Crossrefs

Cf. A000124, A002061, A003215, A062786, A090562.

Sequence in context: A248784 A341337 A067868 * A153803 A083524 A222559

Adjacent sequences: A298757 A298758 A298759 * A298761 A298762 A298763

Keyword

nonn,more

Author

Amiram Eldar, Jan 26 2018

Status

approved