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%I #25 Jan 24 2020 01:05:50
%S 1,2,4,9,19,41,87,193,427,940,2049,4619,10363,22921,50522,111018,
%T 248438,554112,1232067,2723158,6003186,13446356,30050952,66594552,
%U 147234100,324832999,714046741,1585188074,3511557725,7762753394,17129248715,37693951852,82773271861
%N a(n) is equal to a(n-1) plus (a(n-1) written in base n but interpreted in base n+1), with a(1)=1.
%e Given the 5th term in the sequence, the next (6th) term is the 5th term plus the result obtained by taking the 5th term's digits in order in base 6 (the index of the next term) and incrementing the base by 1 without changing the digits.
%e In this example, a(5) = 19 = 31_6; incrementing the base of 31_6 without changing the digits gives 31_7 = 22, and a(6) = a(5) + 22 = 19 + 22 = 41.
%e .
%e digits
%e of a(n-1)
%e a(n-1) interpreted
%e in in base n+1
%e n a(n-1) base n = k k + a(n-1) = a(n)
%e - ------ ------ ----------- -------------------
%e 1 1
%e 2 1 1_2 1_3 = 1 1 + 1 = 2
%e 3 2 2_3 2_4 = 2 2 + 2 = 4
%e 4 4 10_4 10_5 = 5 5 + 4 = 9
%e 5 9 14_5 14_6 = 10 10 + 9 = 19
%e 6 19 31_6 31_7 = 22 22 + 19 = 41
%e 7 41 56_7 56_8 = 46 46 + 41 = 87
%e 8 87 127_8 127_9 = 106 106 + 87 = 193
%t a[n_] := a[n] = a[n-1] + FromDigits[ IntegerDigits[ a[n-1], n], n + 1]; Array[a, 33] (* _Giovanni Resta_, Dec 16 2019 *)
%o (PARI) lista(nn) = {my(a = 1); print1(a, ", "); for (n=2, nn, a += fromdigits(digits(fromdigits(digits(a, n), n+1))); print1(a, ", "););} \\ _Michel Marcus_, Dec 16 2019
%K nonn,base,easy
%O 1,2
%A _Tristan Young_, Dec 15 2019