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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.
2
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Feb 20 2024
STATUS
approved