A253776 Primes representable as x^y + x + y, where x>1, y>1 are integers.

13, 71, 137, 251, 353, 523, 1013, 1033, 2213, 4933, 24421, 32803, 39341, 59063, 78137, 117701, 125053, 140663, 148933, 205441, 274693, 279949, 343073, 371311, 456613, 493121, 524309, 571873, 681563, 912773, 1225153, 1594339, 1953253, 2406241, 2924353, 3241943, 3652421

Offset: 1

Author

Alex Ratushnyak, Jan 12 2015

Keywords

• nonn

Links

• Robert Israel and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 800 terms from Israel)

Crossrefs

Cf. A253775, A253777.

Programs

Maple

N:= 10^6; # to get all terms <= N
A:= select(t -> t <= N and isprime(t), {seq(seq(x^y+x+y, y = 2..floor(log[x](N-x))), x=2..floor(sqrt(N)))}, N):
sort(convert(A,list)); # Robert Israel, Sep 18 2024

PARI

list(lim)=my(v=List()); forstep(y=3,oo,2, if(2^y+y+2>lim, break); for(x=2,oo, my(p=x^y+x+y); if(p>lim, break); if(isprime(p), listput(v,p)))); Set(v) \\ Charles R Greathouse IV, Sep 18 2024