A375912 Primes p such that p*nextprime(p)+1 and p + nextprime(p)+1 are both perfect squares where nextprime(p) is the smallest prime that is larger than p.

3, 11, 59, 179, 311, 419, 2111, 3119, 5099, 21011, 21839, 24419, 30011, 37811, 41759, 44699, 60899, 68819, 83639, 86111, 100799, 135719, 143111, 161879, 163019, 165311, 177011, 210599, 218459, 241511, 273059, 304979, 312839, 437111, 450299, 491039, 584279, 595139, 603899, 637319

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

11 is a term because 11*nextprime(11)+1 = 12^2 and 11 + nextprime(11)+1 = 5^2.

Maple

nn:=10^5:
for n from 1 to nn do:
p:=ithprime(n):q:=nextprime(p):p1:=sqrt(p*q+1):p2:=sqrt(q+p+1):
 if floor(p1) = p1 and floor(p2)=p2
  then
  printf(`%d, `, p):
  else
 fi:
od:

Mathematica

Select[Partition[Prime[Range[100000]], 2, 1], IntegerQ[Sqrt[#[[1]] + #[[2]] + 1]] && IntegerQ[Sqrt[#[[1]]*#[[2]] + 1]] &][[;; , 1]] (* Amiram Eldar, Sep 02 2024 *)

Crossrefs

Intersection of A001359 and A242384.

Sequence in context: A242384 A225809 A267607 * A319248 A340865 A290484

Adjacent sequences: A375909 A375910 A375911 * A375913 A375914 A375915

Keyword

nonn

Author

Michel Lagneau, Sep 02 2024

Status

approved