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%I #25 Nov 28 2021 12:34:20
%S 1,9,3,7,5,8,2,82,84,6,4,64,66,46,48,28,49,19,37,39,55,57,58,59,67,68,
%T 69,73,75,76,77,78,79,85,86,87,88,89,91,93,94,95,96,97,98,99,191,919,
%U 193,737,373,739,194,646,464,648,282,828,284,649,195,555,557,375,558,285,559,196,466,467,376,468,286
%N Lexicographically earliest sequence of distinct terms such that the sum of two neighboring digits is not a palindrome.
%C The digit zero must be absent of the sequence.
%e The 1st digit of the seq + the 2nd digit = (1 + 9) = 10 (not a palindrome);
%e the 2nd digit of the seq + the 3rd digit = (9 + 3) = 12 (not a palindrome);
%e the 3rd digit of the seq + the 4th digit = (3 + 7) = 10 (not a palindrome);
%e the 4th digit of the seq + the 5th digit = (7 + 5) = 12 (not a palindrome); etc.
%t q[n_] := n < 10 || !AnyTrue[Plus @@@ Partition[IntegerDigits[n], 2, 1], PalindromeQ]; a[1] = 1; a[n_] := a[n] = Module[{k = 2, t = Array[a, n - 1]}, While[!q[k] || MemberQ[t, k] || PalindromeQ[Mod[a[n - 1], 10] + First[IntegerDigits[k]]], k++]; k]; Array[a, 100] (* _Amiram Eldar_, Nov 28 2021 *)
%Y Cf. A236689.
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Nov 27 2021
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