A239439 Smallest number between consecutive odd primes whose sum of prime factors is a minimum.

4, 6, 8, 12, 15, 18, 20, 24, 30, 32, 40, 42, 45, 48, 54, 60, 64, 70, 72, 75, 81, 84, 90, 100, 102, 105, 108, 112, 120, 128, 135, 138, 144, 150, 154, 162, 165, 168, 175, 180, 189, 192, 196, 198, 200, 216, 225, 228, 231, 234, 240, 243, 256, 260, 264, 270, 275

Offset

1,1

Comments

The prime factors are counted with multiplicity, as in A001414.

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

For n = 1, the 1st and 2nd odd prime numbers are 3 and 5. 4 is the only number between them. So a(1) = 4;
...
For n = 10, the 10th and 11th odd 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;
32 and 36 have the minimum sum of prime factors, i.e., 10, and 32 is the smaller number of the two.  So a(10) = 32.

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; s = i]; , {i, p1 + 1, p2 - 1}]; s, {n, 2, 58}]

Crossrefs

Cf. A000040, A001414.

Sequence in context: A096629 A334468 A020177 * A325601 A310662 A231569

Adjacent sequences: A239436 A239437 A239438 * A239440 A239441 A239442

Keyword

nonn,easy

Author

Lei Zhou, Mar 18 2014

Status

approved