A038869 -id:A038869 - cp's OEIS frontend

A118071 Primes which are the sum of a twin prime pair + 1.

13, 37, 61, 277, 397, 457, 541, 1201, 1237, 1321, 1621, 1657, 2557, 2857, 3217, 4057, 4177, 4261, 4621, 5101, 5581, 6337, 6661, 6781, 7057, 7537, 8101, 8317, 8461, 8521, 8677, 9277, 9601, 10837, 10957, 11317, 11701, 12541, 12601, 12721, 13381, 13921

Offset: 1

Jonathan Vos Post, May 11 2006

			a(1) = 13 = 5 + 7 + 1 where (5,7) is a twin prime pair.
a(2) = 37 = 17 + 19 + 1.
a(3) = 61 = 29 + 31 + 1.
a(4) = 277 = 137 + 139 + 1.
a(5) = 397 = 197 + 199 + 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A000040, A001359, A006512, A054735, A038869.

Select[Total/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]] == 2&]+1,PrimeQ] (* Harvey P. Dale, Jul 25 2019 *)

is(n)=n%12==1 && isprime(n) && isprime(n\2-1) && isprime(n\2+1) \\ Charles R Greathouse IV, Jan 21 2015

{A001359(k) + A006512(k) + 1} INTERSECT {A000040}.
{A054735(k) + 1} INTERSECT {A000040}.
{2*A001359(k) + 3} INTERSECT {A000040}.
{2*A006512(k) - 1} INTERSECT {A000040}. - Juri-Stepan Gerasimov, Apr 26 2010

More terms added by Vladimir Joseph Stephan Orlovsky, Mar 10 2009

A177336 Greater of twin primes p such that 3*p-2 is also greater of twin primes.

Original entry on oeis.org

5, 7, 61, 271, 1951, 3001, 6361, 11491, 11551, 14551, 18541, 19891, 21841, 31081, 32911, 32971, 33331, 33601, 42571, 42841, 50461, 53551, 58111, 68881, 70201, 74611, 79231, 80911, 93811, 96331, 98911, 104311, 109141, 114601, 121021, 125791

Offset: 1

Juri-Stepan Gerasimov, May 07 2010

nonn

			a(1) = 5 because 5 is the greater of the twin primes (3, 5) and 3*5 - 2 = 13 is the greater of the twin primes (11, 13).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A006512, A038869, A088878.

Cf. A132929, A174920.

[p:p in PrimesInInterval(3,130000)| IsPrime(p-2) and IsPrime(3*p-2) and IsPrime(3*p-4)]; // Marius A. Burtea, Dec 23 2019

Select[Range[3, 126000], And @@ PrimeQ[{#, # - 2, 3# - 2, 3# - 4}] &] (* Amiram Eldar, Dec 23 2019 *)

From Wesley Ivan Hurt, May 03 2022: (Start)
a(n) = A132929(n) + 1.
a(n) = A174920(n) + 2. (End)

Definition corrected, 1231 and 1483 inserted, and all values above 3000 corrected by R. J. Mathar, May 10 2010
Terms corrected to match definition by D. S. McNeil, May 10 2010
Name corrected by Amiram Eldar, Dec 23 2019

A307833 Smallest k > 1 such that A014574(n)*k is adjacent to a prime.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 3, 5, 3, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 4, 3, 3, 2, 2, 2, 2, 2, 3, 2, 4, 3, 2, 2, 2, 3, 6, 3, 2, 2, 2, 3, 4, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 4, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 5, 2, 4, 4, 4, 4, 3, 2, 5, 2, 3, 4, 2, 4, 4, 2, 2, 2, 4, 2, 6, 4, 2, 2, 5, 4, 6

Offset: 1

Dmitry Kamenetsky, May 01 2019

nonn

It is perhaps surprising that the values in this sequence are so small. For n < 8000 the largest value of a(n) is 20, which occurs for n = 4928. Also for n < 8000, a(n) is 2 on 2449 occasions.

a(n)=2 if and only if A014574(n)+1 is in A038869 or A014574(n)-1 is in A045536. - Robert Israel, Jul 17 2019

			72*5 = 360, which is adjacent to the prime 359, so a(8) = 5.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A014574, A038869, A045536, A307775, A309120.

P:= {seq(ithprime(i),i=1..10^4)}:
A014574:= sort(convert(map(t -> t+1, P intersect map(`-`,P,2)),list)):
f:= proc(m) local k;
  for k from 2 do
    if isprime(k*m-1) or isprime(k*m+1) then return k fi
  od
end proc:
map(f, A014574); # Robert Israel, Jul 17 2019

primeNearQ[n_] := AnyTrue[{-1, 1} + n, PrimeQ]; twinMidQ[n_] := AllTrue[{-1, 1} + n, PrimeQ]; f[n_] := Module[{k = 2}, While[! primeNearQ[k*n], k++]; k]; f /@ Select[Range[10^4], twinMidQ] (* Amiram Eldar, Jul 05 2019 *)

isok2(n) = isprime(n-1) && isprime(n+1);
k(n) = my(k=2); while (! (isprime(n*k-1) || isprime(n*k+1)), k++); k;
lista(nn) = for (n=1, nn, if (isok2(n), print1(k(n), ", "))); \\ Michel Marcus, May 01 2019

a(n) = A309120(A014574(n)). - Robert Israel, Jul 17 2019

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A118071 Primes which are the sum of a twin prime pair + 1.

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A177336 Greater of twin primes p such that 3*p-2 is also greater of twin primes.

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Magma

Mathematica

Formula

Extensions

A307833 Smallest k > 1 such that A014574(n)*k is adjacent to a prime.

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Maple

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