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%I #17 Feb 07 2024 09:01:06
%S 12,0,0,1,2,11,0,0,1,17,1,3,1,3,3,0,2,1,2,10,16,11,0,0,11,6,0,16,0,0,
%T 1,0,2,9,2,0,0,10,7,9,2,0,2,10,1,15,0,10,10,1,15,1,3,7,15,1,6,9,0,0,0,
%U 9,0,0,1,2,2,9,9,0,0,0,2,9,0,8,9,0,1,0,0,8,0,2,9,5,6,14,1,8,1,6,3,7
%N The number of terms beyond the first term in the series described in A369348 but when starting at n.
%C In the first 250000 terms the largest value is a(203564) = 30. See the examples.
%C See A369353 for the numbers that terminate the series with lengths >= 1.
%H Scott R. Shannon, <a href="/A369349/b369349.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 12. See A369348 for further information.
%e a(2) = 0 as there is no number k such that k - 2 = sopfr(k) + sopfr(2).
%e a(5) = 2 as the series when starting at 5 is 5, 18, 36, and there is no number k such that k - 36 = sopfr(k) + sopfr(36).
%e a(203564) = 30 as the series when starting at 203564 is 203564, 279917, 305772, 306383, 307737, 309072, 618538, 1237084, 1547240, 1549668, 1555427, 1689623, 1850460, 1897986, 1978513, 2170033, 2300849, 2307769, 2313234, 4629862, 6952637, 6966959, 7000937, 8032504, 9080469, 9125207, 9266466, 14110329, 28220667, 37702139, 37817849, and there is no number k such that k - 37817849 = sopfr(k) + sopfr(37817849).
%Y Cf. A369348, A001414, A369350, A369351, A369352, A369353.
%K nonn
%O 1,1
%A _Scott R. Shannon_, Jan 21 2024
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