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

Author

Amiram Eldar, Jan 26 2018

Keywords

• nonn
• more

Comments

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

Examples

			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)
		

Links

• Eric Weisstein's World of Mathematics, Centered Polygonal Number
• Wikipedia, Centered polygonal number

Crossrefs

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

Programs

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