A282323 Lesser of twin primes congruent to 17 (mod 30).

17, 107, 137, 197, 227, 347, 617, 827, 857, 1277, 1427, 1487, 1607, 1667, 1697, 1787, 1877, 1997, 2027, 2087, 2237, 2267, 2657, 2687, 3167, 3257, 3467, 3527, 3557, 3767, 3917, 4127, 4157, 4217, 4337, 4517, 4547, 4637, 4787, 4967, 5417, 5477, 5657, 5867, 6197

Offset

1,1

Comments

The union of [this sequence and A282324] is A132242.

The union of [{3, 5}, A282321, this sequence and A060229] is the lesser of twin primes sequence A001359.

The union of [{3, 5, 7}, A282321 to A282326] is the twin primes sequence A001097.

A181605 without the 7. The proof works along the same lines as the proof in A282322. - R. J. Mathar, Feb 14 2017

Number of terms < 10^k: 0, 0, 1, 9, 64, 414, 2734, 19674, 146953, ... - Muniru A Asiru, Jan 09 2018

Links

Muniru A Asiru, Table of n, a(n) for n = 1..3000

Example

From Muniru A Asiru, Jan 25 2018: (Start)
17 is a member because the pair (17, 19) is a twin prime, 17 < 19 and 17 mod 30 = 17.
137 is a member because the pair (137, 139) is a twin prime, 137 < 139 and 137 mod 30 = 17.
197 is a member because the pair (197, 199) is a twin prime, 197 < 199 and 197 mod 30 = 17.
(End)

Maple

a:={}:
for i from 1 to 1229 do
  if isprime(ithprime(i)+2) and ithprime(i) mod 30 = 17 then
    a:={op(a), ithprime(i)}:
  fi:
od:
a;

Mathematica

Select[17 + 30 Range[0, 220], PrimeQ[#] && PrimeQ[# + 2] &] (* Robert G. Wilson v, Jan 09 2018 *)
Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]]==2&&Mod[#[[1]], 30]==17&][[;; , 1]] (* or *) Select[Range[17, 7000, 30], AllTrue[#+{0, 2}, PrimeQ]&] (* Harvey P. Dale, Mar 02 2024 *)

Prog

(Magma) [p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 17 ]; // Vincenzo Librandi, Feb 13 2017
(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim+2, if(q-p==2 && q%30==19, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017
(GAP)
P:=Filtered([1..400000], IsPrime);;
P1:=List(Filtered(Filtered(List([1..Length(P)-1], n->[P[n], P[n+1]]), i->i[2]-i[1]=2), j->j[1] mod 30=17), k->k[1]);; # Muniru A Asiru, Jul 08 2017

Crossrefs

Subset of A001097, A001359, A039949, A132242 and A132247.

Cf. A006512, A232880, A232881, A232882, A282321, A282322, A282324, A282326.

Sequence in context: A121823 A268263 A343706 * A224322 A142321 A007682

Adjacent sequences: A282320 A282321 A282322 * A282324 A282325 A282326

Keyword

nonn

Author

Martin Renner, Feb 11 2017

Status

approved