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A224505 Primes p such that p+1 is the sum of the squares of a pair of twin primes. 1
73, 1801, 3529, 10369, 20809, 103969, 115201, 426889, 649801, 2080801, 2205001, 2654209, 3266569, 3328201, 4428289, 5171329, 10017289, 10672201, 11347849, 14709889, 21780001, 22177801, 28395649, 29675809, 30701449, 32320801, 35583049, 40176649, 41368609 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes in A184417.

Obviously, no prime has the form q^2+(q+2)^2+1, where q and q+2 are twin primes.

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

EXAMPLE

3529 (prime) is in the sequence because 3529+1 = 41^2+43^2, where 41 and 43 are twin primes.

MAPLE

A224505:=proc(q) local a, n;

for n from 1 to q do

  if ithprime(n+1)-ithprime(n)=2 then a:=ithprime(n+1)^2+ithprime(n)^2-1;

  if isprime(a) then print(a); fi; fi;

od; end: A224505(10^6); # Paolo P. Lava, Apr 17 2013

MATHEMATICA

Select[(#[[1]]^2 + #[[2]]^2 - 1) & /@ Select[Partition[Prime[Range[700]], 2, 1], #[[2]] - #[[1]] == 2 &], PrimeQ]

PROG

(MAGMA) [p: r in PrimesUpTo(5000) | IsPrime(r+2) and IsPrime(p) where p is 2*r^2+4*r+3];

CROSSREFS

Cf. A063533 (sums of the squares of a pair of twin primes), A118072 (primes which are sum of a pair of twin primes minus 1), A184417.

Sequence in context: A197216 A197502 A197241 * A217286 A282784 A017789

Adjacent sequences:  A224502 A224503 A224504 * A224506 A224507 A224508

KEYWORD

nonn

AUTHOR

Bruno Berselli, Apr 08 2013

STATUS

approved

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Last modified May 24 03:21 EDT 2017. Contains 286937 sequences.