%I #16 Feb 11 2024 23:45:23
%S 1,0,0,1,2,0,0,0,1,1,1,0,1,0,1,0,2,0,2,0,0,0,0,1,1,1,0,1,0,1,1,0,0,0,
%T 3,0,0,0,0,2,2,0,2,0,1,1,0,0,2,0,0,0,3,0,2,0,1,0,0,0,0,1,0,0,2,0,2,1,
%U 0,1,0,0,2,1,1,2,0,0,1,1,0,1,0,0,0,0,1,0,1,4,0,1,0,0,0,0,0,0,0
%N The number of terms beyond the first term for the series starting at k(1) = n and then iteratively finding the smallest k(i+1) such that k(i+1) - k(i) = sopfr(k(i+1) + k(i)), where i >= 1 and sopfr(m) is the sum of the primes dividing m, with repetition.
%C In the first 500000 terms the largest value is a(443314) = 17. See the examples.
%C See A369357 for the numbers that terminate the series with lengths >= 1.
%H Scott R. Shannon, <a href="/A369354/b369354.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 1 as the series when starting at 1 is 1, 7, and there is no number k such that k - 7 = sopfr(k + 7).
%e a(2) = 0 as there is no number k such that k - 2 = sopfr(k + 2).
%e a(5) = 2 as the series when starting at 5 is 5, 13, 23, and there is no number k such that k - 23 = sopfr(k + 23).
%e a(443314) = 17 as the series when starting at 443314 is 443314, 454409, 454790, 455085, 456828, 474078, 474578, 482330, 482497, 483143, 486180, 486225, 534858, 535155, 535369, 540494, 580542, 581003, and there is no number k such that k - 581003 = sopfr(k + 581003).
%Y Cf. A001414, A369355, A369356, A369357, A369812, A369981, A369348, A369349.
%K nonn
%O 1,5
%A _Scott R. Shannon_, Jan 25 2024