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A270245 Lesser of twin primes such that sum of twin prime pair is the sum of 2 nonzero squares. 0
3, 179, 521, 809, 1619, 1871, 2087, 2339, 3257, 3329, 4049, 4337, 4931, 5651, 5849, 6569, 6659, 6947, 7487, 8009, 8387, 8819, 8999, 10529, 10889, 11699, 12239, 14561, 15137, 16361, 16451, 16649, 17657, 17747, 19079, 19889, 19961, 20231, 20771, 20807, 21059, 22481, 22697, 23039, 23201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

3 is a term because 3 + 5 = 2^2 + 2^2.

179 is a term because 179 + 181 = 6^2 + 18^2.

521 is a term because 521 + 523 = 12^2 + 30^2.

809 is a term because 809 + 811 = 18^2 + 36^2.

MATHEMATICA

Select[Select[Prime@ Range@ 2700, PrimeQ[# + 2] &], Length[PowersRepresentations[2 # + 2, 2, 2] /. {0, _} -> Nothing] > 0 &] (* Michael De Vlieger, Mar 15 2016 *)

PROG

(PARI) isA000404(n)={ for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}

t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}

for(n=1, 1e3, if(isA000404(2*t(n)+2), print1(t(n), ", ")));

CROSSREFS

Cf. A000404, A001359, A054735.

Sequence in context: A198446 A216967 A217443 * A093434 A053291 A013519

Adjacent sequences:  A270242 A270243 A270244 * A270246 A270247 A270248

KEYWORD

nonn

AUTHOR

Altug Alkan, Mar 13 2016

STATUS

approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)