A271348
Primes p such that p + 2*k^2 is prime for at least 10 consecutive values of k starting from k=1.
Original entry on oeis.org
11, 29, 438926021, 1210400879, 7446335849, 31757068151, 33090566651, 33164857769, 40137398219, 45133754591, 46642404071, 100444384301, 114546675671, 144553207691, 159587584529, 161557039991, 166054101539, 210447830009, 227625400031, 236241327599, 254850262949, 272259344081
Offset: 1
11 is a term because 11+2*k^2 gives rise to 10 primes for 10 consecutive values of k starting from 1 (see A050265).
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lst={}; Do[k=1; While[PrimeQ[Prime[n]+2*k^2], k++]; If[k>10, AppendTo[lst, Prime[n]]], {n, 2, 11*10^9}]; lst
Select[Prime[Range[107669*10^5]],AllTrue[#+{2,8,18,32,50,72,98,128,162,200},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run *) (* Harvey P. Dale, Jan 24 2021 *)
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forprime(n=2, 276241327599, k=1; while(isprime(n+2*k^2), k++); (k>10)&&print1(n, ", "))
A271366
Primes of the form 272259344081 + 2*n^2.
Original entry on oeis.org
272259344081, 272259344083, 272259344089, 272259344099, 272259344113, 272259344131, 272259344153, 272259344179, 272259344209, 272259344243, 272259344281, 272259344323, 272259344369, 272259344419, 272259344881, 272259345433, 272259345539, 272259347123, 272259347281, 272259347953
Offset: 1
For n=0, we get 272259344081, which is a prime as determined in A271348.
For n=1, we get 272259344081 + 2*1^2 = 272259344083, which is a prime as determined in A271348.
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Select[Table[272259344081+2*n^2, {n, 0, 100}], PrimeQ]
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for(n=0, 100, isprime(272259344081+2*n^2) && print1(272259344081+2*n^2, ","))
A271819
Primes of the form 159587584529 + 2*n^2.
Original entry on oeis.org
159587584529, 159587584531, 159587584537, 159587584547, 159587584561, 159587584579, 159587584601, 159587584627, 159587584657, 159587584691, 159587584729, 159587584771, 159587585107, 159587585329, 159587585681, 159587585881, 159587586097, 159587586451, 159587586707, 159587586979
Offset: 1
For n=0, we get 159587584529, which is a prime as determined in A271348.
For n=1, we get 159587584529 + 2*1^2 = 159587584531, which is a prime as determined in A271348.
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Select[Table[159587584529+2*n^2, {n, 0, 100}], PrimeQ]
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for(n=0, 100, isprime(159587584529+2*n^2) && print1(159587584529+2*n^2, ", "))
A271820
Primes of the form 236241327599 + 2*n^2.
Original entry on oeis.org
236241327599, 236241327601, 236241327607, 236241327617, 236241327631, 236241327649, 236241327671, 236241327697, 236241327727, 236241327761, 236241327799, 236241327841, 236241328177, 236241328751, 236241330049, 236241331831, 236241332207, 236241332401, 236241333649, 236241334799
Offset: 1
For n=0, we get 236241327599, which is a prime as determined in A271348.
For n=1, we get 236241327599 + 2*1^2 = 236241327601, which is a prime as determined in A271348.
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Select[Table[236241327599+2*n^2, {n, 0, 100}], PrimeQ]
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for(n=0, 100, isprime(236241327599+2*n^2) && print1(236241327599+2*n^2, ", "))
Showing 1-4 of 4 results.
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