A332772 Numbers k > 0 such that 30k +- 7 is prime.

1, 2, 3, 4, 9, 10, 12, 13, 15, 19, 20, 25, 26, 29, 32, 33, 37, 41, 43, 48, 52, 53, 54, 58, 66, 67, 76, 78, 81, 85, 88, 89, 90, 92, 95, 97, 101, 107, 118, 120, 121, 128, 129, 134, 143, 150, 153, 155, 165, 166, 172, 178, 180, 194, 195, 202, 207, 209, 211, 212

Offset

1,2

Comments

Looking for prime factors > 5=prime(3) in 8=A005867(3) candidates mod 30=A002110(3) two candidates in the form 30k +- 7 with k > 0 never belong to a twin prime pair. Twin primes can be (30k-13, 30k-11) A331840, (30k-1, 30k +1) A176114, or (30k+11, 30k+13) A089160.

Links

Table of n, a(n) for n=1..60.

Frank Ellermann, Illustration for A002110, A005867, A038110, A060753

Example

a(4)=4 for prime(30)=113=4*30-7 and prime(31)=127=4*30+7.
a(5)=9 for prime(56)=263=9*30-7 and prime(59)=277=9*30+7.

Mathematica

Select[Range@ 215, AllTrue[30 # + {-7, 7}, PrimeQ] &] (* Michael De Vlieger, Feb 25 2020 *)

Prog

(Rexx)
S = 1
do N = 2 while length( S ) < 255
   if NOPRIME( N * 30 + 7 )   then  iterate N
   if NOPRIME( N * 30 - 7 )   then  iterate N
   S = S || ', ' N
end N
say S

Crossrefs

Cf. A000040, A002110, A005867, A089160, A176114, A331840.

Subsequence of A158573. Prime pairs 30k +- 7 in A329262.

Sequence in context: A047339 A250483 A294485 * A084368 A007498 A073338

Adjacent sequences: A332769 A332770 A332771 * A332773 A332774 A332775

Keyword

nonn,easy

Author

Frank Ellermann, Feb 25 2020

Status

approved