A375912 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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