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Starting with a(1) = 1, a(n) = smallest nonnegative integer not yet in the sequence such that the last digit of a(n-1) plus the first digit of a(n) is equal to 7. The digit 0 is not allowed.
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%I #9 Jul 24 2017 12:53:40

%S 1,6,11,61,62,5,2,51,63,4,3,41,64,31,65,21,66,12,52,53,42,54,32,55,22,

%T 56,13,43,44,33,45,23,46,14,34,35,24,36,15,25,26,16,17

%N Starting with a(1) = 1, a(n) = smallest nonnegative integer not yet in the sequence such that the last digit of a(n-1) plus the first digit of a(n) is equal to 7. The digit 0 is not allowed.

%C The number of terms of this finite sequence is the seventh central polygonal number, n = 43.

%t Module[{a = {1}, k, d = 7}, TimeConstrained[Do[k = 2; While[Or[MemberQ[a, k], MemberQ[IntegerDigits@ k, 0], # != d] &[Mod[a[[n - 1]], 10] + First@ IntegerDigits@ k], k++]; AppendTo[a, k], {n, 2, 100}], 2]; a] (* _Michael De Vlieger_, Jul 14 2017 *)

%Y Cf. A002061, A289283, A289284.

%K nonn,base,fini,full

%O 1,2

%A _Enrique Navarrete_, Jul 01 2017