A216330 Squares equal to the difference between two successive primes of the form n^2+1.

64, 144, 100, 1024, 4900, 10816, 11664, 12544, 18496, 102400, 41616, 46656, 331776, 298116, 44100, 451584, 270400, 141376, 372100, 678976, 504100, 1849600, 524176, 2890000, 3504384, 602176, 685584, 8702500, 1768900, 2160900, 868624, 532900, 624100, 12960000

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Example

64 is in the sequence because 6^2 + 1 = 37, 10^2+1 = 101 and 101 - 37 = 64 is square.

Maple

q:=2:for n from 2 to 100 do:p:=n^2+1:if type(p, prime)=true then x:=p-q:q:=p: z:=sqrt(x):if z=floor(z) then printf(`%d, `, z):else fi:od:

Mathematica

Select[#[[2]]-#[[1]]&/@Partition[Select[Range[2000000]^2+1, PrimeQ], 2, 1], IntegerQ[ Sqrt[#]]&] (* Harvey P. Dale, Nov 08 2017 *)

Crossrefs

Cf. A193558.

Sequence in context: A068410 A250654 A223063 * A110232 A348548 A188244

Adjacent sequences: A216327 A216328 A216329 * A216331 A216332 A216333

Keyword

nonn

Author

Michel Lagneau, Sep 04 2012

Status

approved