OFFSET
1,1
COMMENTS
q is always a Pythagorean prime (A002144).
Semiprimes of the form p*q where p < q such that q divides p^(q+1) + k and (q-p)^(q+1) + k:
k = 1: (this sequence);
k = 2: 6, 33, 119, 247, 451, ...
k = 3: 14, 35, 91, 341, ...
k = 4: 39, 145, 371, ...
For every positive odd number q (whether prime or not), every integer p in 0..q, and every integer k, if q divides p^(q+1) + k, then it necessarily follows that q also divides (q-p)^(q+1) + k; thus, this sequence could be more simply defined as "Semiprimes of the form p*q where p < q such that q divides p^(q+1) + 1." - Jon E. Schoenfield, Dec 07 2016
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
MATHEMATICA
Take[#, 41] &@ Union@ Flatten@ Table[Function[q, q Select[Prime@ Range@ n, Function[p, And[Divisible[p^(q + 1) + 1, q], Divisible[(q - p)^(q + 1) + 1, q]]]]]@ Prime@ n, {n, 600}] (* Michael De Vlieger, Dec 02 2016 *)
PROG
(PARI) list(lim)=my(v=List()); forprime(q=5, lim\2, if(q%4>2, next); forprime(p=2, min(lim\q, q-2), if(Mod(p, q)^(q+1)==-1 && Mod(q-p, q)^(q+1)==-1, listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Dec 02 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Dec 01 2016
STATUS
approved