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A282322 Greater of twin primes congruent to 13 (mod 30). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 11:57 EDT 2019. Contains 328108 sequences. (Running on oeis4.)