A370503 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that sopfr(|a(n) - a(n-1)|) = sopfr(a(n) + a(n-1)) and Omega(|a(n) - a(n-1)|) = Omega(a(n) + a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.

1, 13735, 600, 987, 147, 8517, 1938, 6551, 1086, 384, 689, 9961, 648, 1063, 270, 767, 188, 28, 142, 12, 107, 97843, 5130, 5818, 1212, 3221, 1280, 1601, 166, 1909, 174547, 15178, 9484, 432, 787, 360, 913, 634, 1621, 4, 46, 409, 9679, 378, 743, 330, 911, 224, 365, 85, 13747, 316, 1114, 1669, 19517

Offset

1,2

Comments

The fixed points begin 1, 306, 13442, 24566, 30607, 53557, 65136; it is likely there are infinitely more. The sequence is conjectured to be a permutation of the positive integers, although it takes many terms for some values to appear, e.g., a(177950) = 9.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

a(2) = 13735 as a(1) = 1 and |13735-1| = 13734, 13735+1 = 13736, and soprf(13734) = 124 = soprf(13736), Omega(13734) = 5 = Omega(13736). No smaller number satisfies these requirements.
a(492) = 2 as a(491) = 427 and |427-2| = 425, 427+2 = 429, and soprf(425) = 27 = soprf(429), Omega(425) = 3 = Omega(429).

Crossrefs

Cf. A001414, A001222, A370504, A370502, A369348.

Sequence in context: A236708 A205259 A370504 * A235184 A270639 A031807

Adjacent sequences: A370500 A370501 A370502 * A370504 A370505 A370506

Keyword

nonn

Author

Scott R. Shannon, Feb 20 2024

Status

approved