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A306102
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Numbers that are the difference of two positive squares in at least two ways.
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4
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15, 21, 24, 27, 32, 33, 35, 39, 40, 45, 48, 51, 55, 56, 57, 60, 63, 64, 65, 69, 72, 75, 77, 80, 81, 84, 85, 87, 88, 91, 93, 95, 96, 99, 104, 105, 108, 111, 112, 115, 117, 119, 120, 123, 125, 128, 129, 132, 133, 135, 136, 140, 141, 143, 144, 145, 147, 152, 153, 155, 156
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Numbers n such that A100073(n) >= 2; see there for more information and formulas.
In sequence A058957 the smaller square is allowed to be zero, therefore it lists all squares > 4 (m^2 - 0^2 = ((m^2+1)/2)^2 - ((m^2-1)/2)^2 if odd, = (m^2/4+1)^2 - (m^2/4-1)^2 if even) in addition to the terms given here, which already comprise squares (64, 144, ...) having more representations than these "trivial" ones. - M. F. Hasler, Jul 11 2018
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LINKS
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Table of n, a(n) for n=1..61.
Geoffrey Campbell, Numbers that are the difference of two squares in two or more ways, Number Theory group on LinkedIn, July 8, 2018.
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FORMULA
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A306102 = { n = 2k+1 | A056924(n) > 1 } U { n = 4k | A056924(n/4) > 1 }. - M. F. Hasler, Jul 10 2018
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MATHEMATICA
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Select[Range@156, Length@ FindInstance[x^2 - y^2 == # && x>y>0, {x, y}, Integers, 2] == 2 &] (* Giovanni Resta, Jul 10 2018 *)
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PROG
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(PARI) select( is(n)=A100073(n)>1, [1..200]) \\ M. F. Hasler, Jul 10 2018
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CROSSREFS
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Cf. A100073, A058957, A056924, A000290.
Contains A306103 and A306104 as subsequences.
Sequence in context: A033708 A343821 A294171 * A177024 A325037 A154545
Adjacent sequences: A306099 A306100 A306101 * A306103 A306104 A306105
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KEYWORD
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nonn
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AUTHOR
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Geoffrey B. Campbell (Geoffrey.Campbell(AT)anu.edu.au), Jul 10 2018
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STATUS
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approved
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