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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307562 Numbers k such that both 6*k + 1 and 6*k + 7 are prime. 3
 1, 2, 5, 6, 10, 11, 12, 16, 17, 25, 26, 32, 37, 45, 46, 51, 55, 61, 62, 72, 76, 90, 95, 100, 101, 102, 121, 122, 125, 137, 142, 146, 165, 172, 177, 181, 186, 187, 205, 215, 216, 220, 237, 241, 242, 247, 257, 270, 276, 277, 282, 290, 291, 292, 296, 297, 310, 311, 312, 331, 332, 335, 347, 355, 356, 380, 381, 390 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There are 138 such numbers between 1 and 1000. Prime pairs that differ by 6 are called "sexy" primes. Other prime pairs that differ by 6 are of the form 6n - 1 and 6n + 5. Numbers in this sequence are those which are not 6cd - c - d - 1, 6cd - c - d, 6cd + c + d - 1 or 6cd + c + d, that is, they are not (6c - 1)d - c - 1, (6c - 1)d - c, (6c + 1)d + c - 1 or (6c + 1)d + c. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Sally M. Moite, “Primeless” Sieves for Primes and for Prime Pairs Which Differ by 2m, vixra:1903.0353 (2019). EXAMPLE a(3) = 5, so 6(5) + 1 = 31 and 6(5) + 7 = 37 are both prime. MATHEMATICA Select[Range[400], AllTrue[6 # + {1, 7}, PrimeQ] &] (* Michael De Vlieger, Apr 15 2019 *) PROG (PARI) isok(n) = isprime(6*n+1) && isprime(6*n+7); \\ Michel Marcus, Apr 16 2019 CROSSREFS For the primes see A023201, A046117. Similar sequences for twin primes are A002822, A067611, for "cousin" primes A056956, A186243. Intersection of A024899 and A153218. Cf. also A307561, A307563. Sequence in context: A184418 A112967 A244731 * A109150 A004202 A013647 Adjacent sequences: A307559 A307560 A307561 * A307563 A307564 A307565 KEYWORD nonn AUTHOR Sally Myers Moite, Apr 14 2019 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.

Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)