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A350510
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Square array read by descending antidiagonals: A(n,k) is the least number m such that the base-n expansion of m contains the base-n expansions of 1..k as substrings.
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2
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1, 2, 1, 6, 5, 1, 12, 11, 6, 1, 44, 38, 27, 7, 1, 44, 95, 75, 38, 8, 1, 92, 285, 331, 194, 51, 9, 1, 184, 933, 1115, 694, 310, 66, 10, 1, 1208, 2805, 4455, 3819, 1865, 466, 83, 11, 1, 1256, 7179, 17799, 16444, 8345, 3267, 668, 102, 12, 1
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OFFSET
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2,2
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LINKS
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FORMULA
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For k < n, A(n,k) = A(n,k - 1)*n + k = Sum_{i=1..k} i*(n^(k - i)).
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EXAMPLE
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Square array begins:
n/k|| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
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2 || 1 | 2 | 6 | 12 | 44 | 44 | 92 | 184 |
3 || 1 | 5 | 11 | 38 | 95 | 285 | 933 | 2805 |
4 || 1 | 6 | 27 | 75 | 331 | 1115 | 4455 | 17799 |
5 || 1 | 7 | 38 | 194 | 694 | 3819 | 16444 | 82169 |
6 || 1 | 8 | 51 | 310 | 1865 | 8345 | 55001 | 289577 |
7 || 1 | 9 | 66 | 466 | 3267 | 22875 | 123717 | 947260 |
8 || 1 | 10 | 83 | 668 | 5349 | 42798 | 342391 | 2177399 |
9 || 1 | 11 | 102 | 922 | 8303 | 74733 | 672604 | 6053444 |
10 || 1 | 12 | 123 | 1234 | 12345 | 123456 | 1234567 | 12345678 |
11 || 1 | 13 | 146 | 1610 | 17715 | 194871 | 2143588 | 23579476 |
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MATHEMATICA
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T[n_, k_]:=(m=0; While[!ContainsAll[Subsequences@IntegerDigits[++m, n], IntegerDigits[Range@k, n]]]; m); Flatten@Table[T[1+i, j+1-i], {j, 9}, {i, j}] (* Giorgos Kalogeropoulos, Jan 09 2022 *)
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PROG
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(PARI) A350510_rows(n, k, N=0)= my(L=List(concat(apply(z->fromdigits([1..z], n), [1..n-1]), if(n>2, fromdigits(concat([1, 0], [2..n-1]), n), []))), T1(x)=digits(x, n), T2(x)=fromdigits(x, n), A(x)=my(S=T1(x)); setbinop((y, z)->T2(S[y..z]), [1..#S]), N=if(N, N, L[#L]), A1=A(N)); while(#L<k, while(!vecmin(apply(z->setsearch(A1, z), [1..#L+1])), A1=A(N++)); listput(L, N)); Vec(L)
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CROSSREFS
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The first n - 1 terms of rows: 2: A047778, 3: A048435, 4: A048436, 5: A048437, 6: A048438, 7: A048439, 8: A048440, 9: A048441, 10: A007908, 11: A048442, 12: A048443, 13: A048444, 14: A048445, 15: A048446, 16: A048447.
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KEYWORD
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AUTHOR
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STATUS
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approved
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