A385724 The least integer of n consecutive numbers where each has its sum of prime factors, with multiplicity, being a prime.

17, 2, 5, 10, 1547, 8837, 1293224, 52445796, 3267037, 896531141, 183208285259

Offset: 1

Author

Zhining Yang, Jul 08 2025

Keywords

• nonn
• more

Comments

According to Primepuzzles, puzzle 445:

a(10) = 896531141 given by Carlos Rivera.

a(11) = 183208285259 given by Jens Kruse Andersen.

Examples

			a(4) = 10 because 10=2*5, 11=11, 12 = 2^2*3, 13 = 13 and sum of prime factors of the four consecutive numbers are all primes : 2 + 5 = 7, 11, 2 + 2 + 3 = 7, 13.
		

Links

• Fang, Can we find that the sum of prime factors of each of twelve consecutive positive integers is a prime number?
• G. L. Honaker, Jr., Prime Curio 183208285259.
• Carlos Rivera, Puzzle 445. Consecutive integers with prime SPF, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A100118, A337310.

Programs

Mathematica

f[n_] := PrimeQ@Total[Times @@@ FactorInteger[n]]; a = Table[0, 6];
c = 0; Do[If[c == 0, s = n]; If[f[n] == False, If[a[[c]] == 0, a[[c]] = s]; c = 0, c++], {n, 2, 10000}]; a