A306808 An irregular fractal sequence: underline a(n) iff the sum [a(n-1) + a(n)] is a palindrome; all underlined terms rebuild the starting sequence.
1, 9, 3, 1, 11, 2, 9, 4, 3, 1, 12, 5, 7, 6, 8, 10, 13, 14, 15, 16, 18, 17, 19, 20, 21, 22, 11, 23, 24, 25, 26, 27, 29, 28, 30, 31, 2, 9, 32, 33, 34, 35, 36, 37, 38, 40, 4, 3, 1, 39, 41, 42, 43, 12, 44, 45, 46, 47, 48, 49, 51, 52, 50, 5, 53, 54, 55, 57, 56, 58, 59, 7, 60, 6, 61, 62, 63, 64, 65, 67, 66, 68, 69, 8, 70, 72, 71, 73, 74
Offset: 1
Examples
S starts with a(1) = 1 and a(2) = 9 Can we duplicate a(1) to form a(3)? No, as a(2) + a(3) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(2) + X] is not a palindrome. We get a(3) = 3. Can we duplicate a(1) to form a(4)? Yes, as a(3) + a(4) = 4, which is a palindrome. We get a(4) = 1. Can we duplicate a(2) to form a(5)? No, as a(4) + a(5) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(4) + X] is not a palindrome; we get a(5) = 11. Can we duplicate a(2) to form a(6)? No, as a(5) + a(6) would be 20 and 20 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(5) + X] is not a palindrome; we get a(6) = 2. Can we duplicate a(2) to form a(7)? Yes, as [a(6) + a(7)] = 11, which is a palindrome. We get a(7) = 9. Etc.
Links
- Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002
Crossrefs
Cf. A306803 (which is obtained by replacing palindrome by prime in the definition).
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