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A370502
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)), where sopfr(k) is the sum of the primes dividing k, with repetition.
3
1, 11, 53, 15, 57, 7, 47, 8, 41, 13, 143, 17, 3, 33, 159, 45, 171, 21, 119, 24, 123, 39, 125, 148, 236, 115, 10, 38, 25, 95, 121, 158, 192, 497, 42, 213, 18, 70, 138, 12, 68, 4, 44, 31, 131, 19, 5, 55, 209, 268, 239, 56, 34, 2, 22, 106, 30, 114, 14, 71, 6, 66, 318, 90, 342, 225, 683, 187
OFFSET
1,2
COMMENTS
The fixed points begin 1, 8, 78, 314, 1373, 8822, 10247, 21935; it is likely there are infinitely more. The sequence is conjectured to be a permutation of the positive integers.
LINKS
EXAMPLE
a(5) = 57 as a(4) = 15 and sopfr(|57 - 15|) = sopfr(42) = 12, while sopfr(57 + 15) = sopfr(72) = 12.
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Feb 20 2024
STATUS
approved