A127837 Numbers k such that ((k+1)^k-1)/k^2 is a prime.

2, 3, 5, 17, 4357

Offset

1,1

Comments

All terms are primes. Corresponding primes of the form ((k+1)^k-1)/k^2 are listed in A128466 = 2, 7, 311, 7563707819165039903, ... .

It seems that if p is in the sequence then the first three numbers k such that k^2 divides (p+1)^k-1 are: 1, p & ((p+1)^p-1)/p. 2 is in the sequence and the first three terms of A127103 are : 1, 2 & ((2+1)^2-1)/2; 3 is in the sequence and the first three terms of A127104 are : 1, 3 & ((3+1)^3-1)/3; 5 is in the sequence and the first three terms of A127106 are : 1, 5 & ((5+1)^5-1)/5.

No other terms below 20000. - Max Alekseyev, Apr 25 2007

Links

Table of n, a(n) for n=1..5.

Example

4357 is in the sequence because (4358^4357-1)/4357^2 is prime.

Crossrefs

Cf. A128466, A037205, A060072, A060073, A058128, A128456, A127103, A127104, A127106, A128398.

Sequence in context: A092506 A275159 A127063 * A253646 A004249 A268210

Adjacent sequences: A127834 A127835 A127836 * A127838 A127839 A127840

Keyword

hard,more,nonn

Author

Farideh Firoozbakht and Alexander Adamchuk, Mar 13 2007

Status

approved