A057999 a(n) is smallest prime such that a(n)-1 is a proper multiple of a(n-1)-1, with a(0) = 2.

2, 3, 5, 13, 37, 73, 433, 1297, 2593, 10369, 72577, 508033, 1524097, 12192769, 73156609, 146313217, 438939649, 2633637889, 23702740993, 142216445953, 1991030243329, 37829574623233, 416125320855553, 1664501283422209, 6658005133688833, 126502097540087809, 506008390160351233

Offset: 0

Author

Henry Bottomley, Nov 02 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..576

Crossrefs

Cf. A036012, A046966, A046972, A058000.

Programs

Mathematica

a[0] = 2; a[n_] := a[n] = Module[{k = 2*a[n - 1] - 2}, While[! PrimeQ[k + 1], k += (a[n - 1] - 1)]; k + 1]; Array[a, 25, 0] (* Amiram Eldar, Jan 19 2023 *)

Formula

a(n) = 1 + Product_{i=1..n} A036012(i) = a(n-1) * A036012(n) + 1 - A036012(n).