A239440 The minimal value of A001414(i) where prime(n) < i < prime(n+1).

4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 11, 11, 11, 12, 12, 14, 12, 13, 12, 14, 13, 14, 22, 15, 13, 15, 14, 14, 14, 28, 14, 15, 20, 14, 19, 16, 17, 15, 16, 15, 18, 19, 16, 15, 16, 26, 21, 21, 16, 15, 16, 22, 20, 16, 21, 18, 52, 16, 17, 22, 22, 18, 16, 18, 21

Offset

2,1

Links

Lei Zhou, Table of n, a(n) for n = 2..10001

Example

At n = 2, the second and third prime numbers are 3 and 5. 4 is the only number between them. 4=2^2, 2*2=4. So a(1) = 4;
...
At n = 11, the 11th and 12th prime numbers are 31 and 37. Testing from 32 to 36:
  32 = 2^5, sum of prime factors = 2*5 = 10;
  33 = 3*11, sum of prime factors = 3+11 = 14;
  34 = 2*17, sum of prime factors = 2+17 = 19;
  35 = 5*7, sum of prime factors = 5+7 = 12;
  36 = 2^2*3^2, sum of prime factors = 2*2+3*2 = 10;
The smallest sum of prime factors of these numbers is 10.  So a(11) = 10.

Mathematica

Table[p1 = Prime[n]; p2 = Prime[n + 1]; a = p2; Do[f = FactorInteger[i]; l = Length[f]; sum = 0; Do[sum = sum + f[[j, 1]]*f[[j, 2]], {j, 1, l}]; If[sum < a, a = sum], {i, p1 + 1, p2 - 1}]; a, {n, 2, 68}]

Crossrefs

Cf. A000040, A001414, A239439.

Sequence in context: A014553 A227422 A121855 * A248355 A178053 A090925

Adjacent sequences: A239437 A239438 A239439 * A239441 A239442 A239443

Keyword

nonn,easy

Author

Lei Zhou, Mar 18 2014

Status

approved