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

1,1

Comments

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

Links

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

Formula

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

Maple

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

Mathematica

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 *)

Crossrefs

Sequence in context: A316589 A178127 A307472 * A031929 A161487 A121947

Adjacent sequences: A209616 A209617 A209618 * A209620 A209621 A209622

Keyword

nonn

Author

Lekraj Beedassy, Mar 21 2012

Status

approved