A181606 -id:A181606 - 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

A181604 Twin primes ending in 3.

Original entry on oeis.org

3, 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

Offset: 1

Omar E. Pol, Nov 01 2010

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Cf. A001097, A181603, A181605, A181606.

isA181604 := proc(p)
    if isprime(p) and (isprime(p-2) or isprime(p+2)) then
        if modp(p,10) = 3 then
            true;
        else
            false;
        end if ;
    else
        false;
    end if;
end proc: # R. J. Mathar, Feb 14 2017

Select[Prime@Range@700, Mod[ #, 10] == 3 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)

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

A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

Original entry on oeis.org

11, 29, 41, 71, 107, 149, 197, 239, 281, 431, 569, 827, 1019, 1031, 1061, 1289, 1451, 1667, 1997, 2081, 2111, 2237, 2309, 2657, 2969, 3299, 3329, 3359, 3527, 3821, 4019, 4127, 4229, 4241, 4517, 5849, 6269, 6659, 6761, 7457, 7559, 8597

Offset: 1

Karl V. Keller, Jr., Jan 10 2015

nonn

Primes p such that (p, p+2) and (p+30, p+32) are twin prime pairs.
This sequence is a subsequence of A001359 (lesser of twin primes).
The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).
The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).
The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).

			For n=11, the numbers 11, 13, 41, 43, are primes.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000
Eric Weisstein's World of Mathematics, Prime Quadruplet.
Eric Weisstein's World of Mathematics, Twin Primes
Wikipedia, Twin prime

Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).

a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* Michael De Vlieger, Jan 11 2015 *)

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+30) and isprime(n+32): print(n,end=', ')

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A181605 Twin primes ending in 7.

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A181603 Twin primes ending in 1.

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A181604 Twin primes ending in 3.

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A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

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