A090788 -id:A090788 - cp's OEIS frontend

A090781 Numbers that can be expressed as the difference of the squares of primes in just one distinct way.

5, 16, 21, 24, 40, 45, 48, 96, 112, 117, 144, 160, 165, 192, 264, 280, 285, 288, 336, 352, 357, 504, 520, 525, 648, 816, 832, 837, 936, 952, 957, 1152, 1344, 1360, 1365, 1368, 1440, 1656, 1672, 1677, 1752, 1824, 1840, 1845, 1872, 1968, 2184, 2200, 2205, 2328

Offset: 1

Ray Chandler, Feb 14 2004

nonn

			5 = 3^2 - 2^2.

T. D. Noe, Table of n, a(n) for n=1..908

Cf. A078667, A090788, A090782, A090785.

With[{nn=100},Take[Sort[Transpose[Select[Tally[Last[#]-First[#]&/@ Subsets[ Prime[Range[nn]]^2,{2}]],Last[#]==1&]][[1]]],nn]] (* Harvey P. Dale, Apr 05 2014 *)

from sympy import primerange
from collections import Counter
def aupto(limit):
  sqps = [p*p for p in primerange(1, limit//2+1)]
  ways = Counter(b-a for i, a in enumerate(sqps) for b in sqps[i+1:])
  return sorted(k for k in ways if k <= limit and ways[k] == 1)
print(aupto(2328)) # Michael S. Branicky, May 16 2021

A090782 Numbers that can be expressed as the difference of the squares of primes in just three distinct ways.

Original entry on oeis.org

120, 168, 312, 408, 480, 552, 600, 672, 720, 1008, 1200, 1800, 2160, 2472, 2832, 2880, 3312, 3672, 4560, 5040, 5640, 6120, 6480, 6528, 7248, 7320, 7752, 7872, 8160, 8352, 8400, 8712, 8880, 9048, 9768, 9960, 10032, 10200, 10320, 10488, 10608, 10848

Offset: 1

Ray Chandler, Feb 14 2004

nonn

			120 = 13^2-7^2 = 17^2-13^2 = 31^2-29^2.

Cf. A078667, A090788, A090781.

A092000 Numbers that can be expressed as the difference of the squares of primes in exactly four distinct ways.

Original entry on oeis.org

240, 792, 912, 1248, 2040, 2280, 2760, 3528, 3720, 3960, 4080, 4440, 4680, 4872, 5160, 5520, 5880, 6600, 6720, 6960, 7080, 8520, 8568, 8760, 9072, 9120, 9672, 9912, 10248, 10440, 11088, 11592, 11832, 11880, 12408, 12480, 12720, 13200, 13560

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			240 = 17^2-7^2 = 19^2-11^2 = 23^2-17^2 = 61^2-59^2

Cf. A090781, A090782, A090788, A092001-A092020.

A092020 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-four distinct ways.

Original entry on oeis.org

5383560, 5811960, 6126120, 8410920, 9110640, 10581480, 11124120, 11411400, 13573560, 14894880, 16936920, 18976440, 19503120, 19838280, 20060040, 23589720, 24929520, 28930440, 29004360, 29789760, 30084600, 31143840

Offset: 1

Ray Chandler, Feb 22 2004

nonn

Cf. A090781, A090782, A090788, A092000-A092019.

a(6)-a(22) from Donovan Johnson, Nov 26 2008

A092001 Numbers that can be expressed as the difference of the squares of primes in exactly five distinct ways.

Original entry on oeis.org

1560, 2640, 3120, 4200, 5928, 6072, 6840, 7560, 7800, 10080, 10560, 11400, 11760, 12240, 12600, 13440, 15288, 15600, 15840, 17808, 20592, 20832, 21120, 21528, 21912, 22848, 25680, 25872, 26208, 27840, 29232, 29400, 29640, 30192, 30240

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			1560 = 41^2-11^2 = 43^2-17^2 = 71^2-59^2 = 83^2-73^2 =
197^2-193^2

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

A092019 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-three distinct ways.

Original entry on oeis.org

5542680, 7283640, 7759752, 8168160, 8888880, 10297560, 11379480, 12852840, 14700840, 15236760, 16290120, 16888872, 18050760, 18276720, 18334680, 19477920, 20034840, 20420400, 21519960, 22085448, 22998360, 23848440

Offset: 1

Ray Chandler, Feb 22 2004

nonn

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

a(6)-a(22) from Donovan Johnson, Nov 26 2008

A092002 Numbers that can be expressed as the difference of the squares of primes in exactly six distinct ways.

Original entry on oeis.org

840, 1320, 1680, 2520, 3192, 3432, 4920, 5208, 5280, 5712, 6552, 6888, 9360, 11928, 16008, 19152, 19992, 25200, 29568, 31080, 35880, 38280, 38640, 40920, 41832, 45240, 47880, 48360, 48720, 51240, 51480, 53040, 56280, 57288, 61320, 63240

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			840 = 31^2-11^2 = 37^2-23^2 = 41^2-29^2 = 47^2-37^2 = 73^2-67^2 =
107^2-103^2

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

Take[Transpose[Select[Tally[Sort[Last[#]-First[#]&/@(Subsets[ Prime[ Range[ 2000]],{2}]^2)]],Last[#]==6&]][[1]],40] (* Harvey P. Dale, Nov 17 2013 *)

A092003 Numbers that can be expressed as the difference of the squares of primes in exactly seven distinct ways.

Original entry on oeis.org

1848, 3360, 4368, 7392, 16632, 19320, 26520, 28560, 32760, 34320, 36960, 38760, 44520, 52080, 54600, 57720, 62040, 65208, 68880, 69960, 73920, 75768, 78120, 79560, 82992, 83160, 86520, 89760, 95760, 106080, 108240, 108528, 115368

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			1848 = 47^2-19^2 = 53^2-31^2 = 73^2-59^2 = 83^2-71^2 = 157^2-151^2 = 233^2-229^2 = 463^2-461^2.

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

A092004 Numbers that can be expressed as the difference of the squares of primes in exactly eight distinct ways.

Original entry on oeis.org

7728, 17160, 25080, 26040, 30360, 35112, 42840, 50160, 53592, 56760, 63840, 65520, 67320, 68640, 79800, 90480, 93912, 95880, 98280, 105672, 106680, 112560, 120360, 135408, 135960, 139080, 139128, 140448, 148512, 150360, 154440, 158928

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			7728 = 97^2-41^2 = 107^2-61^2 = 113^2-71^2 = 173^2-149^2 =
283^2-269^2 = 487^2-479^2 = 647^2-641^2 = 1933^2-1931^2

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

A092005 Numbers that can be expressed as the difference of the squares of primes in exactly nine distinct ways.

Original entry on oeis.org

9240, 15960, 22440, 27720, 39480, 50232, 62160, 72072, 80808, 84840, 85272, 92568, 99528, 108360, 111720, 112728, 124488, 127680, 138600, 141360, 151032, 155400, 160440, 174720, 182280, 186648, 192192, 210672, 224400, 237048, 245520

Offset: 1

Ray Chandler, Feb 22 2004

nonn

			9240 = 97^2-13^2 = 101^2-31^2 = 103^2-37^2 = 107^2-47^2 =
127^2-83^2 = 131^2-89^2 = 179^2-151^2 = 467^2-457^2 = 2311^2-2309^2

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

cp's OEIS Frontend

A090781 Numbers that can be expressed as the difference of the squares of primes in just one distinct way.

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A090782 Numbers that can be expressed as the difference of the squares of primes in just three distinct ways.

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A092000 Numbers that can be expressed as the difference of the squares of primes in exactly four distinct ways.

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A092020 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-four distinct ways.

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A092001 Numbers that can be expressed as the difference of the squares of primes in exactly five distinct ways.

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A092019 Numbers that can be expressed as the difference of the squares of primes in exactly twenty-three distinct ways.

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A092002 Numbers that can be expressed as the difference of the squares of primes in exactly six distinct ways.

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A092003 Numbers that can be expressed as the difference of the squares of primes in exactly seven distinct ways.

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A092004 Numbers that can be expressed as the difference of the squares of primes in exactly eight distinct ways.

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Author

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A092005 Numbers that can be expressed as the difference of the squares of primes in exactly nine distinct ways.

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