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A277534
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Least hypotenuse, c, of a Primitive Pythagorean Triangle (PPT) such that the difference between it, c, and its greater leg, b, is n; or 0 if no such PPT exists.
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1
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5, 17, 0, 0, 65, 0, 0, 29, 65, 185, 0, 0, 169, 0, 0, 0, 221, 333, 0, 0, 273, 0, 0, 0, 157, 481, 0, 0, 1189, 0, 0, 641, 1353, 629, 0, 0, 1517, 0, 0, 425, 1681, 777, 0, 0, 1845, 0, 0, 0, 205, 925, 0, 0, 2173, 0, 0, 0, 2337, 1073, 0, 0, 2501, 0, 0, 0, 2665, 1221, 0, 0, 2829, 0, 0, 1405, 2993, 1369, 0
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OFFSET
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1,1
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COMMENTS
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n = 1, 2, 5, 8, 9, 10, 13, 17, 18, 21, 25, ..., satisfies the first criterion;
a(n) = 0 for n = 3, 4, 6, 7, 11, 12, 14, 15, 16, 19, 20, 22, 23, 24, ..., ;
a(n) = 0 for 5832 of the first 10000 terms;
a(8n) = 0 for 832 of the first 10000 terms;
a(8n) = 0 for n: 2, 3, 6, 7, 8, 10, 11, 12, 14, 15, 18, 19, 22, 23, 24, ..., ;
a(8n+1) > 0;
a(8n+2) > 0; a linear 2nd-order recurrence: a(n) = 2*a(n-1) - a(n-2) with a(1) = 185 & a(2) = 333;
a(8n+3) = 0;
a(8n+4) = 0;
a(8n+5) > 0;
a(8n+6) = 0;
a(8n+7) = 0;
Prime terms: 5, 17, 29, 157, 641, 3821, 4201, 17749, 21601, 31981, 38273, 44789, 61129, 66173, 72161, 100673, 108541, 114553, 121421, 142973, 165541, 173777, 182141, 204733, 213881, 225889, 235493, 281837, ..., .
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LINKS
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EXAMPLE
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a(1) is 5 since the PPT (3,4,5) satisfies the first stated criterion; a(2) is 17 since the PPT (8,15,17) satisfies the first stated criterion; a(3) = 0 since there exists no PPT that satisfies the stated criteria; etc.
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MATHEMATICA
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f[n_] := FindInstance[ a^2 + b^2 == c^2 && Mod[c, 4] == 1 && 0 < a < b < c && c - b == n, {a, b, c}, Integers][[1, 3, 2, 1, 1, 3]] + 1 /. 1 + {}[[1, 3, 2, 1, 1, 3]] -> 0; f[1] = 5; Array[f, 75]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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