

A252231


Primes of the form (p+q)^2 + pq, where p and q are consecutive primes.


1



31, 79, 179, 401, 719, 1619, 3371, 8819, 12491, 15671, 23801, 25919, 28871, 32801, 95219, 118571, 154871, 161999, 190121, 266801, 322571, 364499, 375371, 449951, 524831, 725801, 772229, 796001, 820109, 994571, 1026029, 1053401, 1081121, 1225109, 1326089, 1415039
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OFFSET

1,1


LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..12799


EXAMPLE

79 is in the sequence because (3+5)^2 + 3*5 = 79, which is prime.
401 is in the sequence because (7+11)^2 + 7*11 = 401, which is prime.


MAPLE

count:= 0:
p:= 2:
while count < 100 do
q:= nextprime(p);
x:= (p+q)^2+p*q;
if isprime(x) then
count:= count+1;
a[count]:= x;
fi;
p:= q;
od:
seq(a[i], i=1..count); # Robert Israel, Dec 16 2014


MATHEMATICA

Select[Table[(Prime[n] + Prime[n+1])^2 + Prime[n]Prime[n+1], {n, 100}], PrimeQ[#] &]
Select[Total[#]^2+Times@@#&/@Partition[Prime[Range[100]], 2, 1], PrimeQ] (* Harvey P. Dale, Sep 06 2020 *)


PROG

(PARI) s=[]; for(k=1, 100, p=prime(k); q=prime(k+1); t=(p+q)^2 + p*q; if(isprime(t), s=concat(s, t))); s


CROSSREFS

Cf. A000040, A007645, A003136, A243761, A252017.
Sequence in context: A139855 A139901 A242777 * A044169 A044550 A055810
Adjacent sequences: A252228 A252229 A252230 * A252232 A252233 A252234


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Dec 15 2014


STATUS

approved



