A209618 -id:A209618 - cp's OEIS frontend

A209619 Primes separated from their previous adjacent primes by a composite number of successive composites.

149, 191, 251, 293, 347, 419, 431, 557, 587, 641, 701, 719, 797, 821, 839, 929, 1031, 1049, 1061, 1151, 1163, 1181, 1259, 1361, 1409, 1481, 1637, 1709, 1733, 1811, 1847, 1889, 1949, 1973, 2027, 2039, 2063, 2099, 2129, 2153, 2237, 2267, 2333, 2503, 2531, 2579

Offset: 1

Lekraj Beedassy, Mar 21 2012

nonn

a(1) = 149 is the first prime separated from its previous prime (139) by a composite number (9) of successive composites, namely, 148, 147, 146, 145, 144, 143, 142, 141, 140.

Primes p such that nextprime(p) - p - 1 is composite. - Jahangeer Kholdi, Nov 27 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000

N:= 3000: # to get all entries <= N
Primes:= select(isprime,[seq(2*i+1,i=1..(N-1)/2)]):
Q:= map(t -> (t>2) and not isprime(t-1), Primes[2..-1] - Primes[1..-2]):
zip(proc(p,q) if q then p else NULL fi end proc, Primes[2..-1],Q); # Robert Israel, Nov 28 2014

ps = Prime[Range[500]]; pos = Position[Differences[ps] - 1, ?(# > 1 && ! PrimeQ[#] &)]; ps[[Flatten[pos + 1]]] (* _T. D. Noe, Mar 21 2012 *)
Transpose[Select[Partition[Prime[Range[400]], 2, 1], CompositeQ[#[[2]] - #[[1]] - 1] &]][[2]] (* Harvey P. Dale, Aug 05 2014 *)
Select[Prime[Range[375]], NextPrime[#] - # - 1 > 1 && !PrimeQ[NextPrime[#] - # - 1] &] (* Jahangeer Kholdi, Nov 27 2014 *)

a(n) = A151800(A209618(n)).

A209623 Primes separated from their adjacent next primes by a prime number of successive composites.

Original entry on oeis.org

7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 151, 157, 163, 167, 173, 193, 199, 211, 223, 229, 233, 251, 257, 263, 271, 277, 293, 307, 313, 317, 331, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 433, 439, 443

Offset: 1

Lekraj Beedassy, Mar 10 2012

nonn

a(1) = 7 is the first prime separated from the next prime (11) by a prime number (3) of successive composites, namely, 8, 9, 10.

K. D. Bajpai, Table of n, a(n) for n = 1..8000

Cf. A046933, A209618, A098015.

Select[Prime[Range[100]], PrimeQ[NextPrime[#] - # - 1] &] (* T. D. Noe, Mar 12 2012 *)

cp's OEIS Frontend

A209619 Primes separated from their previous adjacent primes by a composite number of successive composites.

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