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A299118 Squares s such that prime(s) + 2 is a square. 0
1, 4, 9, 7745089 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Primes corresponding to the first four squares are 2, 7, 23, and 136866599. The sequence may be finite.

There may be no square s such that prime(s) + 1 is square (none was found up to 10^9).

This is a Diophantine problem of the form f(n^2) + A = m^2, where f(x) = prime(x), and the simplest case of A = 1 has probably no solutions unlike the same case with f(x) = primepi(x) that may even have an infinite number of solutions.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

prime(4) + 2 = 7 + 2 = 9, and both 4 and 9 are squares.

MATHEMATICA

Select[Range[10^4]^2, IntegerQ@Sqrt[Prime[#] + 2] &]

PROG

(PARI) for(n=1, 10^4, issquare(prime(n^2)+2)&&print1(n^2 ", "))

CROSSREFS

Cf. A000290 (squares), A000040 (primes), A011757 (primes with square indices).

Sequence in context: A260305 A229338 A111443 * A276272 A331450 A051499

Adjacent sequences:  A299115 A299116 A299117 * A299119 A299120 A299121

KEYWORD

nonn,more

AUTHOR

Waldemar Puszkarz, Feb 02 2018

STATUS

approved

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Last modified August 5 19:40 EDT 2021. Contains 346488 sequences. (Running on oeis4.)