A350510 - OEIS

A350510

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.

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Table of n, a(n) for n=2..56.

Davis Smith, Upper bounds for A350510(n, k) and various conjectured patterns.

FORMULA

For k < n, A(n,k) = A(n,k - 1)*n + k = Sum_{i=1..k} i*(n^(k - i)).

A(n,n) = A049363(n).

A(n,2) = A057544(n).

For n > 3, A(n,3) = A102305(n).

A(n,n - 1) = A023811(n).

EXAMPLE

Square array begins:

n/k|| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

================================================================|

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 |

MATHEMATICA

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 *)

PROG

(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)

CROSSREFS

Cf. A023811, A035239, A049363, A056744, A057544, A061845, A102305.

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.

Sequence in context: A145960 A205455 A338135 * A259332 A108767 A046817

Adjacent sequences: A350507 A350508 A350509 * A350511 A350512 A350513

KEYWORD

nonn,base,tabl

AUTHOR

Davis Smith, Jan 02 2022

STATUS

approved