The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A249077 Primes of the form n^2 + k such that n^2 - k is also prime, where -n < k < n. 0
 3, 5, 7, 11, 13, 19, 31, 41, 61, 67, 73, 79, 83, 89, 97, 103, 137, 139, 149, 151, 157, 181, 193, 199, 211, 223, 227, 239, 241, 271, 311, 317, 331, 337, 349, 373, 421, 433, 439, 443, 449, 461, 607, 619, 631, 643, 661, 691, 719, 739, 757, 811, 823, 829, 853, 859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Members of a pair (a, b) of primes such that a < b and the distances from a and b to the nearest square above a (or below b) are equal. The only prime of the form n^2 + 1 (A002496) in the sequence is 5. Is this sequence infinite? LINKS Table of n, a(n) for n=1..56. FORMULA A prime p is in the sequence if and only if 2*A053187(p)-p is prime. EXAMPLE 2^2-1=3, 2^2+1=5, both prime. 8^2-3=61, 8^2+3=67, both prime. MAPLE g:= proc(t, m) if isprime(m+t) and isprime(m-t) then (m+t, m-t) else NULL fi end proc: `union`(seq(map(g, {\$1..n-1}, n^2), n=2..100)); # if using Maple 11 or earlier, uncomment the next line # sort(convert(%, list)); # Robert Israel, Oct 31 2014 PROG (Magma) lst:=[]; for m in [1..28] do r:=m*(m+1)+1; s:=(m+1)^2; for a in [r..s-1] do if IsPrime(a) then b:=2*s-a; if IsPrime(b) then Append(~lst, a); Append(~lst, b); end if; end if; end for; end for; Sort(lst); (PARI) for(n=1, 859, if(issquare(n), x=ps=n; until(issquare(x), x++); ns=x); if(isprime(n), if(n-ps

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

Last modified December 3 17:32 EST 2023. Contains 367540 sequences. (Running on oeis4.)