The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137270 Primes p such that p^2 - 6 is also prime. 4
3, 5, 7, 13, 17, 23, 47, 53, 67, 73, 83, 97, 107, 113, 167, 193, 197, 263, 293, 317, 367, 373, 383, 457, 463, 467, 487, 503, 557, 593, 607, 643, 647, 673, 677, 683, 773, 787, 797, 823, 827, 857, 877, 887, 947, 1033, 1063, 1087, 1103, 1187, 1193, 1223, 1303 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Each of the primes p = 2,3,5,7,13 has the property that the quadratic polynomial phi(x) = x^2 + x - p^2 takes on only prime values for x = 1,2,...,2p-2; each case giving exactly one repetition, in phi(p-1) = -p and phi(p) = p.
The only common term in A062718 and A137270 is 5. - Zak Seidov, Jun 16 2015
REFERENCES
F. G. Frobenius, Uber quadratische Formen, die viele Primzahlen darstellen, Sitzungsber. d. Konigl. Acad. d. Wiss. zu Berlin, 1912, 966 - 980.
LINKS
FORMULA
A000040 INTERSECT A028879. - R. J. Mathar, Mar 16 2008
EXAMPLE
The (2 x 7 - 2) -1 = 11 primes given by the polynomial x^2 + x - 7^2 for x = 1, 2, ..., 2 x 7 - 2 are -47, -43, -37, -29, -19, -7, 7, 23, 41, 61, 83, 107.
MAPLE
isA028879 := proc(n) isprime(n^2-6) ; end: isA137270 := proc(n) isprime(n) and isA028879(n) ; end: for i from 1 to 300 do if isA137270(ithprime(i)) then printf("%d, ", ithprime(i)) ; fi ; od: # R. J. Mathar, Mar 16 2008
MATHEMATICA
Select[Prime[Range[2, 300]], PrimeQ[#^2-6]&] (* Harvey P. Dale, Jul 24 2012 *)
PROG
(Magma) [p: p in PrimesUpTo(1350) | IsPrime(p^2-6)]; // Vincenzo Librandi, Apr 14 2013
CROSSREFS
Sequence in context: A372141 A262100 A171566 * A071111 A177070 A247018
KEYWORD
nonn,easy
AUTHOR
Ben de la Rosa and Johan Meyer (meyerjh.sci(AT)ufa.ac.za), Mar 13 2008
EXTENSIONS
Corrected and extended by R. J. Mathar, Mar 16 2008
STATUS
approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)