A282322 Greater of twin primes congruent to 13 (mod 30).

13, 43, 73, 103, 193, 283, 313, 433, 463, 523, 643, 823, 883, 1033, 1063, 1093, 1153, 1303, 1453, 1483, 1723, 1873, 1933, 2083, 2113, 2143, 2383, 2593, 2713, 2803, 3253, 3373, 3463, 3583, 3673, 3823, 3853, 4003, 4093, 4243, 4273, 4423, 4483, 4723, 4933, 5023, 5233, 5443, 5503, 5653, 5743

Offset

1,1

Comments

The union of [A282321 and this sequence] is A132241.

The union of [{5, 7}, this sequence, A282324 and A282326] is the greater of twin primes sequence A006512.

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

A181604 without the 3. [Proof: working mod 10 we see that each value here is in A181604. For the other direction: Except 3 all twin primes in A181604 are upper twin primes; they cannot be lower twin primes because the upper ones would be multiples of 5. The twin primes in A181604 could be == 3 (mod 30) or == 13 (mod 30) or == 23 (mod 30). The first case is excluded because they would be multiples of 3; the third case is excluded because the lower twin primes would be == 21 (mod 30) and also multiples of 3. So only the case == 13 (mod 30) remains.] - R. J. Mathar, Feb 14 2017

Number of terms < 10^k for k >= 1: 0, 3, 13, 67, 401, 2736, 19797, 146841, 1141217, 9137078, ..., . - Robert G. Wilson v, Jan 07 2018

Links

Muniru A Asiru, Table of n, a(n) for n = 1..20000

Maple

a:={}:
for i from 1 to 1229 do
  if isprime(ithprime(i)-2) and ithprime(i) mod 30 = 13 then
    a:={op(a), ithprime(i)}:
  fi:
od:
a;

Mathematica

Select[13 + 30 Range[0, 200], PrimeQ[# - 2] && PrimeQ[#] &] (* Robert G. Wilson v, Jan 07 2018 *)

Prog

(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim, if(q-p==2 && q%30==13, listput(v, q)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017

Crossrefs

Subset of A001097, A006512, A132233, A132241 and A132247.

Cf. A001359, A232880, A232881, A232882, A282321, A282323, A282324, A282326.

Sequence in context: A264900 A082369 A132233 * A031382 A187677 A082040

Adjacent sequences: A282319 A282320 A282321 * A282323 A282324 A282325

Keyword

nonn

Author

Martin Renner, Feb 11 2017

Status

approved