A296441 Array A(n, k) = G_k(n) where G_k(n) is the k-th term of the Goodstein sequence of n, read by antidiagonals.
0, 0, 1, 0, 0, 2, 0, 0, 2, 3, 0, 0, 1, 3, 4, 0, 0, 0, 3, 26, 5, 0, 0, 0, 2, 41, 27, 6, 0, 0, 0, 1, 60, 255, 29, 7, 0, 0, 0, 0, 83, 467, 257, 30, 8, 0, 0, 0, 0, 109, 775, 3125, 259, 80, 9, 0, 0, 0, 0, 139, 1197, 46655, 3127, 553, 81, 10, 0, 0, 0, 0, 173, 1751, 98039, 46657, 6310, 1023, 83, 11
Offset: 0
Examples
| n\k | 0 1 2 3 4 5 6 7 8 9 ... |-----|------------------------------------------------------------------------ | 0 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | 1 | 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... | 2 | 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, ... | 3 | 3, 3, 3, 2, 1, 0, 0, 0, 0, 0, ... | 4 | 4, 26, 41, 60, 83, 109, 139, 173, 211, 253, ... | 5 | 5, 27, 255, 467, 775, 1197, 1751, 2454, 3325, 4382, ... | 6 | 6, 29, 257, 3125, 46655, 98039, 187243, 332147, 555551, 885775, ... | ... |
Links
- Iain Fox, Antidiagonals n = 0..20 of array, flattened
- Eric Weisstein's World of Mathematics, Hereditary Representation
- Eric Weisstein's World of Mathematics, Goodstein Sequence
- Eric Weisstein's World of Mathematics, Goodstein's Theorem
- Wikipedia, Hereditary base-n notation
- Wikipedia, Goodstein sequence
- Wikipedia, Goodstein's Theorem
Crossrefs
n-th row: A000004 (n=0), A000007 (n=1), A215409 (n=3), A056193 (n=4), A266204 (n=5), A266205 (n=6), A271554 (n=7), A271555 (n=8), A271556 (n=9), A271557 (n=10), A271558 (n=11), A271559 (n=12), A271560 (n=13), A271561 (n=14), A222117 (n=15), A059933 (n=16), A271562 (n=17), A271975 (n=18) A211378 (n=19), A271976 (n=20).
k-th column: A001477 (k=0), A056004 (k=1), A057650 (k=2), A059934 (k=3), A059935 (k=4), A059936 (k=5), A271977 (k=6), A271978 (k=7), A271979 (k=8), A271985 (k=9), A271986 (k=10).
G_n(n) = A266201(n) (main diagonal of array).
Programs
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PARI
B(n, b)=sum(i=1, #n=digits(n, b), n[i]*(b+1)^if(#n
Comments