A242459 Maximal differences of A029707.

1, 2, 3, 4, 6, 12, 20, 24, 27, 29, 42, 54, 72, 75, 103, 128, 131, 151, 153, 162, 164, 181, 204, 208, 209, 211, 237, 265, 285, 286, 326, 335, 340, 356, 368, 392, 409, 432, 439, 441, 444, 446

Offset: 1

Author

Jani Melik, May 15 2014

Keywords

• nonn
• more

Crossrefs

Cf. A000720, A001359, A027833, A029707, A054691.

Programs

Mathematica

nextLesserTwinPrime[p_Integer] := Block[{q = p + 2}, While[ NextPrime@ q - q > 2, q = NextPrime@ q]; q]; p = 2; q = 3; px = 1; qx = 2; mxd = 0; tpx = 0; lst = {}; While[p <
5090000001, d = qx - px; If[ d > mxd, mxd = d; AppendTo[ lst, d]; Print@ d]; p = q; px = qx; q = nextLesserTwinPrime@ q; qx = PrimePi@ q; tpx++]; lst (* Robert G. Wilson v, May 21 2014 *)

Sage

def A242459_list(n) :
   a = [ 1 ]
   st = 3
   for i in (4..n) :
      if (nth_prime(i+1)-nth_prime(i) == 2) :
         if i-st > a[len(a)-1] :
            a.append(i-st)
         st = i
   return(a)
A242459_list(10^(5))

Formula

a(n) = primepi(next(A054691(n-1))) - primepi(A054691(n-1)) + 1 for n >= 2, where primepi = A000720 and next(k) is the least lesser of twin primes that is larger than k. - Amiram Eldar, May 19 2024

Extensions

a(20)-a(28) from Robert G. Wilson v, May 21 2014

a(29)-a(42) from Amiram Eldar, May 19 2024