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A209619 Primes separated from their previous adjacent primes by a composite number of successive composites. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)