login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271348 Primes p such that p + 2*k^2 is prime for at least 10 consecutive values of k starting from k=1. 4
11, 29, 438926021, 1210400879, 7446335849, 31757068151, 33090566651, 33164857769, 40137398219, 45133754591, 46642404071, 100444384301, 114546675671, 144553207691, 159587584529, 161557039991, 166054101539, 210447830009, 227625400031, 236241327599, 254850262949, 272259344081 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number 10 was chosen as a threshold as the smallest two digit number. You can choose other numbers and if they are less than 12, the first terms of sequences analogous to this one will be those in A165234.

There are 20 primes like that among the first 10^10 of them. The second term, 29, generates 28 primes (A007641). Sixteen others, including 11 (A050265), generate only 10 primes, while three produce 11 primes. These three are: 33164857769 (see also A165234), 159587584529, and 236241327599. The first term among the second 10^10 of primes is 254850262949. Then there is 272259344081 (mentioned in A165234) that generates 13 primes.

All these primes end with 1 or 9 and are congruent to 5 mod 6.

LINKS

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Prime-generating Polynomial

EXAMPLE

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).

MATHEMATICA

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

PROG

(PARI) forprime(n=2, 276241327599, k=1; while(isprime(n+2*k^2), k++); (k>10)&&print1(n, ", "))

CROSSREFS

Cf. A000040 (primes), A050265, A007641, A271366, A271818, A271819, A271820 (examples of sequences of primes generated by terms of this sequence), A165234.

Sequence in context: A282137 A027758 A285992 * A057739 A146751 A162734

Adjacent sequences:  A271345 A271346 A271347 * A271349 A271350 A271351

KEYWORD

nonn

AUTHOR

Waldemar Puszkarz, Apr 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)