A174957
Lesser of twin primes p1 such that p1*p2-4 and p1*p2-6 are twin prime numbers.
Original entry on oeis.org
5, 11, 1031, 2711, 3851, 4421, 5867, 8837, 10067, 12041, 12251, 12611, 17957, 21491, 21521, 22037, 22481, 23537, 32141, 32411, 42641, 48311, 48731, 49367, 50261, 53231, 60167, 72167, 77417, 80147, 80447, 81047, 87641, 88337, 90527, 95231
Offset: 1
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lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1*p2-4]&&PrimeQ[p1*p2-6],(*Print[p1];*)AppendTo[lst,p1]],{n,8!}];lst
ltp[{a_,b_}]:=b-a==2&&AllTrue[a*b-{4,6},PrimeQ]; Select[Partition[Prime[ Range[ 10000]],2,1],ltp][[All,1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 07 2017 *)
A354682
Interprimes that are products of two successive primes.
Original entry on oeis.org
6, 15, 667, 1517, 9797, 123197, 233273, 522713, 627239, 826277, 974153, 988027, 1127843, 1162003, 1209991, 2624399, 2637367, 3493157, 4235339, 4384811, 4460543, 6827753, 7784099, 10916407, 11370383, 17065157, 25009997, 26347493, 29964667, 32330587, 32387477, 33419957, 34809991, 35354867, 37088099
Offset: 1
a(3) = 667 is a term because 667 = (661 + 673)/2 = 23*29 where 661 and 673 are successive primes and 23 and 29 are successive primes.
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R:= NULL: count:= 0:
q:= 2:
while count < 50 do
p:= q; q:= nextprime(q);
r:= p*q;
if prevprime(r)+nextprime(r)=2*r then
R:= R, r; count:= count+1;
fi
od:
R;
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Select[Table[Prime[n]*Prime[n + 1], {n, 1, 800}], Plus @@ NextPrime[#, {-1, 1}] == 2*# &] (* Amiram Eldar, Jun 03 2022 *)
Select[Times@@@Partition[Prime[Range[1000]],2,1],(NextPrime[#]+NextPrime[#,-1])/2==#&] (* Harvey P. Dale, Nov 03 2024 *)
Showing 1-2 of 2 results.
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