A330303 - OEIS

%I #24 Dec 13 2019 19:45:35

%S 1,905,18895,56287,3296885,53892169,496722329,1415354159,110690012639

%N Least start of a run of exactly n consecutive odd numbers that are all de Polignac numbers (A006285).

%e a(2) = 905 since both 905 and 905 + 2 = 907 are de Polignac numbers.

%e a(3) = 18895 since 18895, 18895 + 2 = 18897 and 18895 + 4 = 18899 are all de Polignac numbers.

%t dePolQ[n_] := AllTrue[n - 2^Range[0, Floor[Log[2, n]]], !PrimeQ[#] &]; max = 5; seq = Table[0, {max}]; count = 0; k = 3; While[count < max, If[dePolQ[k], kk = k + 2; While[dePolQ[kk], kk += 2]; n = (kk - k)/2; If[n <= max && seq[[n]] == 0, count++; seq[[n]] = k]; k = kk + 2, k += 2]]; seq

%Y Cf. A006285, A330284.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Dec 13 2019