A164129 -id:A164129 - cp's OEIS frontend

A164130 Sums s of squares of three consecutive primes, such that s-+2 are primes.

195, 5739, 18459, 32259, 33939, 60291, 74019, 169491, 187131, 244899, 276819, 388179, 783531, 902139, 3588339, 5041491, 5145819, 5193051, 8687091, 9637491, 10227291, 10910019, 11341491, 11757339, 14834379, 15354651, 16115091

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 10 2009

nonn

			5^2 + 7^2 + 11^2 = 195 is a sum of the squared consecutive primes 5, 7 and 11, and 193 and 197 are primes, so 195 is a member of the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A075893, A133529, A133530, A034962, A164129

q:= 2: r:= 3: R:= NULL: count:= 0:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  s:= p^2+q^2+r^2;
  if isprime(s-2) and isprime(s+2) then
    count:= count+1; R:= R,s;
  fi;
od:
R; # Robert Israel, Apr 21 2023

lst={};Do[p=Prime[n]^2+Prime[n+1]^2+Prime[n+2]^2;If[PrimeQ[p-2]&&PrimeQ[p+2], AppendTo[lst,p]],{n,8!}];lst

A133529 INTERSECT A087679. - R. J. Mathar, Aug 27 2009

Comment turned into example by R. J. Mathar, Aug 27 2009

A261748 Primes of the form p^3 - q^3 + r^3 where p, q, r are consecutive primes.

Original entry on oeis.org

19081, 17569, 124561, 284129, 461933, 12994939, 59888791, 136812059, 210687859, 381287213, 430477739, 967646789, 1003292441, 1214844443, 1235842577, 1630956673, 2035265203, 3409511489, 3760252651, 4212399799, 5010219631, 5823581399, 6487158329, 7774729381, 8729833339

Offset: 1

K. D. Bajpai, Aug 30 2015

nonn

Indices of the initial primes p: 8, 9, 14, 18, 20, 51, 76, 96, 108, 128, 133, 166, 168, ..., . - Robert G. Wilson v, Sep 03 2015

			19081 appears in the sequence because 19^3 - 23^3 + 29^3 = 19081 which is prime and 19, 23, 29 are consecutive primes.
17569 appears in the sequence because 23^3 - 29^3 + 31^3 = 17569 which is prime and 23, 29, 31 are consecutive primes.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A000578, A030078, A164129, A165612.

[k: n in [1..1000] | IsPrime(k) where k is (NthPrime(n)^3 - NthPrime(n+1)^3 + NthPrime(n+2)^3)];

Select[Table[(Prime[n]^3 - Prime[n + 1]^3 + Prime[n + 2]^3), {n, 1, 1000}], PrimeQ]
Select[#[[1]]-#[[2]]+#[[3]]&/@Partition[Prime[Range[500]]^3,3,1],PrimeQ] (* Harvey P. Dale, Jul 29 2021 *)

for(n=1, 500, k=(prime(n)^3 - prime(n+1)^3 + prime(n+2)^3 ); if(isprime(k), print1(k, ", ")));

cp's OEIS Frontend

A164130 Sums s of squares of three consecutive primes, such that s-+2 are primes.

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