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, ","))
A271818
Primes of the form 33164857769 + 2*n^2.
Original entry on oeis.org
33164857769, 33164857771, 33164857777, 33164857787, 33164857801, 33164857819, 33164857841, 33164857867, 33164857897, 33164857931, 33164857969, 33164858011, 33164858347, 33164858569, 33164858737, 33164859019, 33164859569, 33164859691, 33164859817, 33164860219, 33164860507, 33164862769, 33164863177, 33164864731, 33164864969, 33164865457, 33164865961, 33164866481, 33164868427, 33164869321
Offset: 1
For n=0, we get 33164857769, which is a prime as determined in A271348.
For n=1, we get 33164857769 + 2*1^2 = 33164857771, which is a prime as determined in A271348.
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Select[Table[33164857769+2*n^2, {n, 0, 100}], PrimeQ]
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for(n=0, 100, isprime(33164857769+2*n^2) && print1(33164857769+2*n^2, ", "))
Showing 1-3 of 3 results.
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