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A330489
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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.
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0
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1, 2, 4, 9, 19, 41, 87, 193, 427, 940, 2049, 4619, 10363, 22921, 50522, 111018, 248438, 554112, 1232067, 2723158, 6003186, 13446356, 30050952, 66594552, 147234100, 324832999, 714046741, 1585188074, 3511557725, 7762753394, 17129248715, 37693951852, 82773271861
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listen;
history;
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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.
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digits
of a(n-1)
a(n-1) interpreted
in in base n+1
n a(n-1) base n = k k + a(n-1) = a(n)
- ------ ------ ----------- -------------------
1 1
2 1 1_2 1_3 = 1 1 + 1 = 2
3 2 2_3 2_4 = 2 2 + 2 = 4
4 4 10_4 10_5 = 5 5 + 4 = 9
5 9 14_5 14_6 = 10 10 + 9 = 19
6 19 31_6 31_7 = 22 22 + 19 = 41
7 41 56_7 56_8 = 46 46 + 41 = 87
8 87 127_8 127_9 = 106 106 + 87 = 193
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MATHEMATICA
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a[n_] := a[n] = a[n-1] + FromDigits[ IntegerDigits[ a[n-1], n], n + 1]; Array[a, 33] (* Giovanni Resta, Dec 16 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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