A090781 -id:A090781 - cp's OEIS frontend

A092015 Numbers that can be expressed as the difference of the squares of primes in exactly nineteen distinct ways.

120120, 513240, 722568, 2348808, 3721872, 4269720, 5442360, 5754840, 6109488, 7549080, 8288280, 9043320, 10986360, 12538680, 13037640, 13813800, 14395920, 15181320, 15408120, 15571920, 15735720, 16151520, 16379160, 16696680

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			120120 = 347^2-17^2 = 349^2-41^2 = 353^2-67^2 = 383^2-163^2 =
421^2-239^2 = 463^2-307^2 = 467^2-313^2 = 499^2-359^2 = 521^2-389^2 =
601^2-491^2 = 757^2-673^2 = 1031^2-971^2 = 1181^2-1129^2 = 1451^2-1409^2 =
2017^2-1987^2 = 2741^2-2719^2 = 4297^2-4283^2 = 5011^2-4999^2 =
15017^2-15013^2.

Cf. A090781, A090782, A090788, A092000-A092020.

a(13)-a(24) from Donovan Johnson, Nov 26 2008

A092016 Numbers that can be expressed as the difference of the squares of primes in exactly twenty distinct ways.

Original entry on oeis.org

885360, 3527160, 3723720, 4444440, 7054320, 8921640, 9304680, 9524760, 9817080, 9849840, 9914520, 10038840, 11152680, 11171160, 12113640, 12543960, 13167000, 13728792, 14108640, 14774760, 15495480, 17264520, 17777760, 17882040

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			885360 = 941^2-11^2 = 947^2-107^2 = 967^2-223^2 = 977^2-263^2 =
991^2-311^2 = 1123^2-613^2 = 1289^2-881^2 = 1979^2-1741^2 = 2213^2-2003^2 =
2473^2-2287^2 = 2719^2-2551^2 = 3323^2-3187^2 = 4391^2-4289^2 =
7933^2-7877^2 = 11087^2-11047^2 = 13037^2-13003^2 = 14771^2-14741^2 =
18457^2-18433^2 = 44273^2-44263^2 = 55339^2-55331^2

Cf. A090781, A090782, A090788, A092000-A092020.

a(12)-a(24) from Donovan Johnson, Nov 26 2008

A092017 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-one distinct ways.

Original entry on oeis.org

2282280, 5165160, 5645640, 5969040, 6754440, 7197960, 8048040, 8075760, 8426880, 8725080, 9267720, 10767120, 11466840, 12235080, 12252240, 12480720, 13508880, 13581960, 13869240, 13901160, 13980120, 14316120, 14665560

Offset: 1

Ray Chandler, Feb 22 2004

nonn

Cf. A090781, A090782, A090788, A092000-A092020.

a(12)-a(23) from Donovan Johnson, Nov 26 2008

A092018 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-two distinct ways.

Original entry on oeis.org

526680, 2106720, 4037880, 4555320, 4772040, 4924920, 7785960, 9988440, 10330320, 11051040, 11843832, 12525240, 12809160, 13093080, 13933920, 14348040, 15222480, 15513960, 16576560, 19634160, 19677840, 19764360

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			526680 = 727^2-43^2 = 733^2-103^2 = 761^2-229^2 = 839^2-421^2 =
863^2-467^2 = 883^2-503^2 = 941^2-599^2 = 1009^2-701^2 = 1123^2-857^2 =
1171^2-919^2 = 1307^2-1087^2 = 1429^2-1231^2 = 1481^2-1291^2 = 1553^2-1373^2
= 1951^2-1811^2 = 2153^2-2027^2 = 3797^2-3727^2 = 6949^2-6911^2 =
7333^2-7297^2 = 9419^2-9391^2 = 11981^2-11959^2 = 14639^2-14621^2

Cf. A090781, A090782, A090788, A092000-A092020.

a(9)-a(22) from Donovan Johnson, Nov 26 2008

A092204 Least number that can be expressed as the difference of the squares of primes in exactly n distinct ways.

Original entry on oeis.org

5, 72, 120, 240, 1560, 840, 1848, 7728, 9240, 21840, 10920, 55440, 236208, 469560, 207480, 175560, 185640, 314160, 120120, 885360, 2282280, 526680, 5542680, 5383560, 6366360, 2042040, 4564560, 5091240, 6440280, 2984520, 7382760

Offset: 1

Robert G. Wilson v and Ray Chandler, Feb 24 2004

nonn

The next entry, a(32) > 10^7, a(33) = 3483480 and a(34) = 4084080.

First entry in A090781, A090788, A090782, A092000-A092020 respectively.

A132329 Numbers that cannot be expressed as the difference of the squares of primes.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Rick L. Shepherd, Aug 19 2007

nonn

Complement of A124865.

Cf. A124865, A090781.

lim=80;sp={4};i=2;Until[Prime[i]^2-(Prime[i]-2)^2>lim,AppendTo[sp,Prime[i]^2];i++];Complement[Range[lim],Union[Differences/@Subsets[sp,{2}]//Flatten]] (* James C. McMahon, Mar 08 2025 *)

cp's OEIS Frontend

A092015 Numbers that can be expressed as the difference of the squares of primes in exactly nineteen distinct ways.

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A092016 Numbers that can be expressed as the difference of the squares of primes in exactly twenty distinct ways.

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A092017 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-one distinct ways.

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A092018 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-two distinct ways.

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A092204 Least number that can be expressed as the difference of the squares of primes in exactly n distinct ways.

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A132329 Numbers that cannot be expressed as the difference of the squares of primes.

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Mathematica