OFFSET
1,1
COMMENTS
Conjecture: a(n)> 0 for all n > 0.
The primes in the sequence are 3, 5, 11, 13, 19, 29, 73, 173, 191,...
The squares in the sequence are 25, 64, 100,...
EXAMPLE
a(1)=13 because 13^2+1 = 170 = 2*5*17 => 170 mod(2+5+17) = 170 mod 24 = 2 = prime(1).
MATHEMATICA
Table[k=0; While[Mod[k^2+1, Plus@@First[Transpose[FactorInteger[k^2+1]]]]!=Prime[n], k++]; k, {n, 50}]
PROG
(PARI) a(n) = {k = 1; while ((m=k^2+1) && (lift(Mod(m, vecsum(factor(m)[, 1]))) != prime(n)) , k++); k; } \\ Michel Marcus, Apr 29 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 28 2016
STATUS
approved