OFFSET
1,2
COMMENTS
Conjecture: The current sequence has infinitely many terms.
This was first mentioned in Remark 2.21 of the linked 2017 paper.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Conjectures on representations involving primes, in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II, Springer Proc. in Math. & Stat., Vol. 220, Springer, Cham, 2017, pp. 279-310. (See also arXiv, arXiv:1211.1588 [math.NT], 2012-2017.)
EXAMPLE
a(2) = 2 with prime(2) = 3 = 1^2 + 2*1^2.
a(3) = 12 with prime(12) = 37 = 5^2 + 12*1^2.
a(4) = 35 with prime(35) = 149 = 3^2 + 35*2^2.
MATHEMATICA
SQ[n_]:=SQ[n]=n>0&&IntegerQ[Sqrt[n]];
tab={}; Do[Do[If[SQ[Prime[m]-m*x^2], tab=Append[tab, m]; Goto[aa]], {x, 1, Sqrt[Prime[m]/m]}]; Label[aa], {m, 1, 3245}]; tab
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 13 2020
STATUS
approved