A181604 -id:A181604 - cp's OEIS frontend

A181605 Twin primes ending in 7.

7, 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

Offset: 1

Omar E. Pol, Nov 01 2010

First disagrees with A092340 at n=26: A092340 contains 2707, but this sequence doesn't. Is this a subsequence of A092340? - Nathaniel Johnston, Jun 25 2011

Yes, it is a subsequence of A092340: see link. - Robert Israel, Apr 13 2021

Robert Israel, Table of n, a(n) for n = 1..10000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
Robert Israel, A181605 is a subsequence of A092340

Cf. A001097, A092340, A181603, A181604, A181606.

[7, op(select(t -> isprime(t) and isprime(t+2), [seq(i,i=17..10000,30)]))]; # Robert Israel, Apr 13 2021

Select[Prime@ Range@ 800, Mod[ #, 10] == 7 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)

A001097 INTERSECT A030432. - R. J. Mathar, Nov 03 2010

More terms from R. J. Mathar and Robert G. Wilson v, Nov 03 2010

A181603 Twin primes ending in 1.

Original entry on oeis.org

11, 31, 41, 61, 71, 101, 151, 181, 191, 241, 271, 281, 311, 421, 431, 461, 521, 571, 601, 641, 661, 811, 821, 881, 1021, 1031, 1051, 1061, 1091, 1151, 1231, 1291, 1301, 1321, 1451, 1481, 1621, 1721, 1871, 1931, 1951, 2081, 2111, 2131, 2141, 2311, 2341, 2381

Offset: 1

Omar E. Pol, Nov 01 2010

These are twin primes == 1 (mod 30) or == 11 (mod 30) or == 21 (mod 30). In the first case they cannot be lower twin primes because the upper ones would be == 3 (mod 30) and divisible by 3. In the second case they cannot be upper twin primes because the lower ones would be == 9 (mod 30) and divisible by 3. The last case is excluded because that implies they are divisible by 3. In summary the upper twin primes in here are given by A282326, the lower twin primes in here by A282321. - R. J. Mathar, Feb 14 2017

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Cf. A001097, A181604, A181605, A181606.

isA181603 := proc(p)
    if isprime(p) and (isprime(p-2) or isprime(p+2)) then
        if modp(p,10) = 1 then
            true;
        else
            false;
        end if ;
    else
        false;
    end if;
end proc:
for n from 1 to 1000 do
    if isA181603(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Feb 14 2017

Select[Prime@ Range@ 360, Mod[ #, 10] == 1 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)
Select[Flatten[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]] == 2&]],Mod[#,10]==1&] (* Harvey P. Dale, Oct 24 2021 *)

More terms from Robert G. Wilson v, Nov 06 2010

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

Original entry on oeis.org

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

Martin Renner, Feb 11 2017

nonn

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

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

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

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

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;

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

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

A181606 Twin primes ending in 9.

Original entry on oeis.org

19, 29, 59, 109, 139, 149, 179, 199, 229, 239, 269, 349, 419, 569, 599, 619, 659, 809, 829, 859, 1019, 1049, 1229, 1279, 1289, 1319, 1429, 1489, 1609, 1619, 1669, 1699, 1789, 1879, 1949, 1999, 2029, 2089, 2129, 2239, 2269, 2309, 2339, 2549, 2659, 2689

Offset: 1

Omar E. Pol, Nov 01 2010

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Cf. A001097, A181603, A181604, A181605.

Union of A060229 and A282324.

filter:= proc(n)
  if not isprime(n) then return false fi;
  if n mod 3 = 1 then isprime(n-2) else isprime(n+2) fi
end proc:
select(filter, [seq(i,i=9..10^4,10)]); # Robert Israel, Nov 19 2023

Select[Prime@ Range@ 800, Mod[ #, 10] == 9 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)
Select[Union[Flatten[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]]==2&]]],Mod[#,10]==9&] (* Harvey P. Dale, May 21 2024 *)

More terms from Robert G. Wilson v, Nov 06 2010

cp's OEIS Frontend

A181605 Twin primes ending in 7.

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A181603 Twin primes ending in 1.

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

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A181606 Twin primes ending in 9.

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