A252800 Primes p such that the next prime appears after a gap greater than 100.

370261, 492113, 1098847, 1349533, 1357201, 1388483, 1444309, 1468277, 1561919, 1664123, 1671781, 1761187, 1775069, 1889831, 1895359, 2010733, 2127163, 2238823, 2242549, 2243987, 2305169, 2314439, 2597981, 2614883, 2637799, 2867107, 2898239, 3064751, 3117299, 3225539

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(1) = 370261 : Nextprime = 370373 : Gap = 370373 - 370261 = 112 which is greater than 100.
a(2) = 492113 : Nextprime = 492227 : Gap = 492113 - 492227 = 114 which is greater than 100.

Maple

count:= 0:
x:= 1:
while count < 40 do
  y:= prevprime(x+101);
  if y = x then
     count:= count+1; A[count]:= x;
     x:= nextprime(x+101);
  else
     x:= y;
  fi
od:
seq(A[i], i=1..count);  # Robert Israel, Dec 26 2014

Mathematica

postGaps = {}; Do[k = Prime[n]; If[NextPrime[k] > (k + 100), AppendTo[postGaps, k]], {n, 250000}]; postGaps
Prime[#]&/@Flatten[Position[Differences[Prime[Range[235000]]], _?(#> 100&)]] (* Harvey P. Dale, Sep 30 2018 *)

Prog

(PARI) s=[]; forprime(p=2, 500000, if(nextprime(p+1)>(p+100), s=concat(s, p))); s

Crossrefs

Cf. A000040.

Sequence in context: A172778 A172666 A251209 * A291638 A219284 A017537

Adjacent sequences: A252797 A252798 A252799 * A252801 A252802 A252803

Keyword

nonn

Author

K. D. Bajpai, Dec 22 2014

Status

approved