OFFSET
1,1
COMMENTS
Numbers of this form are an attempt to generalize Mersenne numbers (see link).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Craig J. Beisel, Can it be shown that numbers of a certain form produce primes more often than expected?, Math StackExchange, November 2019.
MAPLE
N:= 1000: # for terms <= N
P:= select(isprime, [seq(i, i=3..(N+3)/2, 2)]):
S:= {}:
for ip from 1 to nops(P) do
p:= P[ip];
for i from 1 while p^i*3 - (p+3) <= N do
for iq from 1 to ip-1 do
q:= P[iq];
if p^i*q - (p+q) > N then break fi;
for j from 1 do
x:= p^i * q^j - (p+q);
if x > N then break fi;
if isprime(x) then S:= S union {x} fi;
od od od od:
sort(convert(S, list)); # Robert Israel, Aug 25 2025
PROG
(PARI) z=[]; forprime(a=3, 1000, forprime(b=a+2, 1000, for(i=1, 10, for(j=1, 10, y=a+b; x=a^i*b^j-y; if(x<500 && isprime(x) && setsearch(z, x)==0, z=setunion(z, [x])) )))); print(z)
CROSSREFS
KEYWORD
nonn
AUTHOR
Craig J. Beisel, Nov 26 2019
EXTENSIONS
Definition clarified by Robert Israel, Aug 25 2025
STATUS
approved
