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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 07:01 EST 2021. Contains 349567 sequences. (Running on oeis4.)