A252231 Primes of the form (p+q)^2 + pq, where p and q are consecutive primes.
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
Offset: 1
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..12799
Programs
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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 *) -
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