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

Author

Lekraj Beedassy, Mar 21 2012

Keywords

• nonn

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

Programs

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 *)

Formula

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