A374369
Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least m such that n and k differ modulo m.
Original entry on oeis.org
2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 2, 4, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
Offset: 1
Triangle T(n, k) begins:
n n-th row
-- ----------------------------------
1 2
2 3, 2
3 2, 3, 2
4 3, 2, 3, 2
5 2, 3, 2, 3, 2
6 4, 2, 3, 2, 3, 2
7 2, 4, 2, 3, 2, 3, 2
8 3, 2, 4, 2, 3, 2, 3, 2
9 2, 3, 2, 4, 2, 3, 2, 3, 2
10 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
11 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
12 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
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T[n_,k_]:=Module[{m=2},While[Mod[n,m]==Mod[k,m], m++]; m]; Table[T[n,k],{n,13},{k,0,n-1}]//Flatten (* Stefano Spezia, Jul 12 2024 *)
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T(n, k) = { for (m = 2, oo, if ((n%m) != (k%m), return (m););); }
A374383
Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least base b >= 2 where n and k have different sums of digits.
Original entry on oeis.org
2, 2, 3, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 5, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 3, 2, 3, 5, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 4, 2
Offset: 1
Triangle T(n, k) begins:
n n-th row
-- ----------------------------------
1 2
2 2, 3
3 2, 2, 2
4 2, 3, 4, 2
5 2, 2, 2, 3, 2
6 2, 2, 2, 3, 2, 3
7 2, 2, 2, 2, 2, 2, 2
8 2, 3, 3, 2, 3, 2, 2, 2
9 2, 2, 2, 5, 2, 3, 3, 2, 2
10 2, 2, 2, 3, 2, 3, 4, 2, 2, 3
11 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2
12 2, 2, 2, 3, 2, 3, 5, 2, 2, 3, 4, 2
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T[n_,k_]:=Module[{b=2},While[DigitSum[n,b]==DigitSum[k,b], b++]; b]; Table[T[n,k],{n,13},{k,0,n-1}]//Flatten (* Stefano Spezia, Jul 12 2024 *)
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T(n, k) = { for (b = 2, oo, my (d = sumdigits(n, b) - sumdigits(k, b)); if (d, return (b););); }
A374462
Triangle T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) equals the p-adic valuation of n minus the p-adic valuation of k where p is the least prime number such that this quantity is nonzero.
Original entry on oeis.org
1, 1, -1, 2, 1, 2, 1, -1, -1, -2, 1, 1, 1, -1, 1, 1, -1, -1, -2, -1, -1, 3, 2, 3, 1, 3, 2, 3, 2, -1, 1, -2, 2, -1, 2, -3, 1, 1, 1, -1, 1, -1, 1, -2, 1, 1, -1, -1, -2, -1, -1, -1, -3, -2, -1, 2, 1, 2, 1, 2, 1, 2, -1, 2, 1, 2, 1, -1, -1, -2, -1, -1, -1, -3, -2, -1, -1, -2
Offset: 2
Triangle T(n, k) begins:
n n-th row
-- -------------------------------------
2 1
3 1, -1
4 2, 1, 2
5 1, -1, -1, -2
6 1, 1, 1, -1, 1
7 1, -1, -1, -2, -1, -1
8 3, 2, 3, 1, 3, 2, 3
9 2, -1, 1, -2, 2, -1, 2, -3
10 1, 1, 1, -1, 1, -1, 1, -2, 1
11 1, -1, -1, -2, -1, -1, -1, -3, -2, -1
12 2, 1, 2, 1, 2, 1, 2, -1, 2, 1, 2
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T(n, k) = { forprime (p = 2, oo, my (d = valuation(n, p) - valuation(k, p)); if (d, return (d); ); ); }
Showing 1-3 of 3 results.
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