OFFSET
1,1
COMMENTS
a(n) = 1 if and only if prime(n) is a Mersenne prime (A000668). Thus A059305 gives the values of n for which a(n) = 1.
For all n, a(n) exists.
Subsequence of A103953.
For n > 1, a(n) <= ((prime(n)-1)/2)^2, since ((p-1)/2)^2 + p = ((p+1)/2)^2. - Jens Kruse Andersen, Aug 10 2014
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
EXAMPLE
n=1: prime(n)=2, 25 = 5^2 and 25+5=27=3^3;
n=2: prime(n)=3, 1 = 1^2 and 1+3=4=2^2;
n=3: prime(n)=5, 4 = 2^2 and 4+5=9=3^2.
PROG
(PARI) {forprime(p=2, 200, if(ispower(1+p), print1(1", "), n=4; while(!(ispower(n)&&ispower(n+p)), n++); print1(n", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 06 2014
STATUS
approved