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A224888 Primes of the form p^2 + (q-p)^2, where p and q are consecutive primes. 2
5, 13, 29, 293, 997, 6257, 11897, 18773, 19421, 52457, 73477, 109597, 120413, 167381, 192737, 218233, 249017, 292717, 333029, 361237, 398261, 466553, 502781, 546137, 552113, 591377, 635353, 683933, 687341, 704117, 737897, 885517, 966353, 982117, 1018097, 1079621 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes of the form A000040(n)^2 + A001223(n)^2.

Primes of the form A134735(2n-1)^2 + A134735(2n)^2.

Conjecture: a(n) ~ A093343(n).

There are 20421247 members of this sequence below 10^20. - Charles R Greathouse IV, Jul 29 2013

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

c(x) is O( sqrt(x/log x) / log x ), where c(x) is the counting function, the number of terms less than x.

EXAMPLE

3 and 5 are consecutive primes and 3^2 + (5-3)^2 = 9 + 4 = 13 is prime, so 13 is in the sequence.

MATHEMATICA

Select[Table[Prime[n]^2 + (Prime[n + 1] - Prime[n])^2, {n, 200}], PrimeQ] (* Alonso del Arte, Jul 29 2013 *)

PROG

(PARI) p=2; forprime(q=3, 1e4, if(isprime(t=p^2+(q-p)^2), print1(t", ")); p=q) \\ Charles R Greathouse IV, Jul 24 2013

CROSSREFS

Cf. A093343.

Sequence in context: A147492 A182069 A085555 * A256314 A002768 A086522

Adjacent sequences:  A224885 A224886 A224887 * A224889 A224890 A224891

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Jul 24 2013

EXTENSIONS

a(5), a(9)-a(36) from Charles R Greathouse IV, Jul 24 2013

STATUS

approved

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)