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%I #9 Mar 29 2024 08:44:43
%S 1,13735,600,987,147,8517,1938,6551,1086,384,689,9961,648,1063,270,
%T 767,188,28,142,12,107,97843,5130,5818,1212,3221,1280,1601,166,1909,
%U 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
%N 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.
%C 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.
%H Scott R. Shannon, <a href="/A370503/b370503.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%e 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).
%Y Cf. A001414, A001222, A370504, A370502, A369348.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Feb 20 2024
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