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A331272
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Irregular triangle in which row n lists numbers m such that A330073(m,n) = 1.
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1
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1, 5, 25, 4, 125, 20, 625, 3, 100, 104, 3125, 15, 16, 500, 520, 15625, 2, 75, 80, 83, 86, 2500, 2600, 2604, 78125, 10, 12, 13, 375, 400, 415, 416, 430, 433, 12500, 13000, 13020, 390625, 50, 60, 62, 65, 66, 69, 71, 1875, 2000, 2075, 2080, 2083, 2150, 2165, 2166, 62500, 65000, 65100, 65104, 1953125
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OFFSET
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0,2
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COMMENTS
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The last number in row n is 5^n (A000351(n)).
For numbers m and n such that m is in row n, 5*m is in row n + 1 and if m > 10 and m == 10, 15, 20, or 25 (mod 30), then floor(m/6) is in row n + 1.
The conjecture in A330073 claims that every positive integer appears in this triangle.
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LINKS
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FORMULA
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If N is the list of numbers in row n, then the list of numbers in row n + 1 is the union of each number in N multiplied by 5 and numbers floor(x/6) where x is in N, congruent to 0 (mod 5), not congruent to 0 or 5 (mod 30), and floor(x/6) > 1.
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EXAMPLE
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The irregular triangle starts:
0: 1
1: 5
2: 25
3: 4 125
4: 20 625
5: 3 100 104 3125
6: 15 16 500 520 15625
7: 2 75 80 83 86 2500 2600 2604 78125
8: 10 12 13 375 400 415 416 430 433 12500 13000 13020 390625
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PROG
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(PARI) A331272(lim)=my(N=[1], b=-1, RC=5*[2..5]); while(b<lim, b++; print(N); N=vecsort(matconcat(apply(X->if(setsearch(RC, X%30)&&(X>RC[1]), [floor(X/6), 5*X], X*5), N))[1, ]))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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