A088176 -id:A088176 - cp's OEIS frontend

A346675 First differences of A088176.

4, 6, 6, 14, 10, 20, 12, 28, 6, 36, 8, 34, 6, 14, 22, 18, 26, 16, 24, 36, 78, 8, 28, 74, 36, 30, 24, 16, 26, 148, 6, 12, 24, 24, 144, 8, 22, 8, 28, 66, 74, 46, 14, 10, 20, 106, 26, 28, 6, 120, 14, 66, 16, 24, 68, 76, 12, 60, 24, 30, 36, 48, 12, 30, 8, 16, 90, 30

Offset: 1

Luca Santarsiero, Jul 28 2021

Conjecture: each term > 4 appears at least twice.

Every term of the sequence is even, because every term is a difference of two odd primes.

			a(7) = A088176(9) - A088176(8) = 107 - 79 = 28.
p = 14855077 and q = 14856077 are prime numbers such that the respective preceding prime number is the greater of twin primes. No other prime number between p and q has this property. Thus 1000 is a term of the sequence.

Cf. A088176.

Differences[NextPrime/@Select[Prime@Range[500],NextPrime[#,-1]==#-2&]] (* Giorgos Kalogeropoulos, Jul 28 2021 *)

a(n) = A088176(n+2) - A088176(n+1).

A088175 Primes such that the next two primes are a twin prime pair.

Original entry on oeis.org

2, 3, 7, 13, 23, 37, 53, 67, 97, 103, 131, 139, 173, 181, 193, 223, 233, 263, 277, 307, 337, 409, 421, 457, 509, 563, 593, 613, 631, 653, 797, 811, 823, 853, 877, 1013, 1021, 1039, 1051, 1087, 1129, 1223, 1259, 1283, 1297, 1307, 1423, 1447, 1471, 1483, 1601

Offset: 1

Zak Seidov, Sep 22 2003

Primes p such that nextprime(p) + 2 is prime. - Irina Gerasimova, Jun 28 2013

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

Cf. A088176.

[NthPrime(n): n in [1..260] | NthPrime(n+2)-NthPrime(n+1) eq 2]; // Vincenzo Librandi, Nov 18 2014

A088175 := proc(n)
    prevprime(A001359(n)) ;
end proc:
seq(A088175(n),n=1..30) ; # R. J. Mathar, Nov 26 2014

fQ[n_]:=PrimeQ[NextPrime[n]+2];Select[Prime@Range@500,fQ] (* Vladimir Joseph Stephan Orlovsky, Apr 16 2011 *)

is(n)=isprime(n) && isprime(nextprime(n+1)+2) \\ Charles R Greathouse IV, Jun 28 2013

More terms from Ray Chandler, Sep 25 2003

Definition clarified by Irina Gerasimova, Jun 28 2013

A227031 Odd primes such that the previous prime is not the larger part of a twin prime pair.

Original entry on oeis.org

3, 5, 13, 19, 29, 31, 41, 43, 53, 59, 61, 71, 73, 83, 89, 97, 101, 103, 109, 127, 131, 137, 139, 151, 163, 167, 173, 179, 181, 193, 199, 223, 227, 229, 239, 241, 257, 263, 269, 271, 281, 283, 307, 311, 313, 331, 337, 347, 349, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421

Offset: 1

Irina Gerasimova, Jun 28 2013

nonn

This is the complement of A088176 in the set of odd primes. - R. J. Mathar, Jul 04 2013

			a(1) = 3 because 3 is prime and prevprime(3) - 2 = 2 - 2 = 0 is not prime,
a(2) = 5 because 5 is prime and prevprime(5) - 2 = 3 - 2 = 1 is not prime,
a(3) = 13 because 13 is prime and prevprime(13) - 2 = 11 - 2 = 9 is composite.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A088175, A088176.

Select[Prime[Range[2, 100]], Not[PrimeQ[NextPrime[#, -1] - 2]] &] (* Alonso del Arte, Jul 04 2013 *)

is(n)=n>2 && !isprime(precprime(n-2)-2) && isprime(n) \\ Charles R Greathouse IV, Mar 18 2014

a(n) ~ prime(n) ~ n log n. - Charles R Greathouse IV, Jun 28 2013

cp's OEIS Frontend

A346675 First differences of A088176.

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A088175 Primes such that the next two primes are a twin prime pair.

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A227031 Odd primes such that the previous prime is not the larger part of a twin prime pair.

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Keywords

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Examples

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Crossrefs

Programs

Mathematica

PARI

Formula