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 A134969 List of pairs of primes that are separated by the equivalent of 2 quadratic intervals. Both primes are greater than their preceding perfect squares by the same amount, or offset. The respective perfect squares can be both odd, in which case the offset is even, or both even, in which case the offset is odd. 0
 3, 11, 5, 17, 7, 19, 13, 29, 17, 37, 23, 43, 29, 53, 43, 71, 67, 103, 71, 107, 73, 109, 97, 137 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Michael M. Ross What Are Odd Squared, or Biquadratic, Paired Primes? FORMULA PS1 + OfN = P1, PS3 + OfN = P2 where PS1 = first perfect square, PS3 = 3rd perfect square OfN = an equal positive offset from preceding perfect square P1 and P2 = the prime pair EXAMPLE For example, prime pair 97 and 137 have an even offset of 16 from 81 and 121: Interval 1: 9*9 = 81 + 16 = 97 Interval 2: 10*10 = 100 + 16 = 116 Interval 3: 11*11 = 121 + 16 = 137 Prime pair 71 and 107 have an odd offset of 7 from 64 and 100: Interval 1: 8*8 = 64 + 7 = 71 Interval 2: 9*9 = 81 + 7 = 88 Interval 3: 10*10 = 100 + 7 = 107 In all cases there is a complete intermediate quadratic interval (#2). PROG Excel VBA available at http://www.naturalnumbers.org/quadprimes.html#code Demonstrates odd-offset prime-pair distribution with associated twin primes. Limitations: -Only the subset of paired primes for even perfect squares with odd offsets are demonstrated. -Because of the 256-column limitation for an Excel worksheet, data in rows after perfect square 484 are not complete. -Only twin primes that are also paired primes are outlined (in red). CROSSREFS Sequence in context: A084466 A084462 A156320 * A139686 A212782 A130537 Adjacent sequences:  A134966 A134967 A134968 * A134970 A134971 A134972 KEYWORD nonn,tabf AUTHOR Michael M. Ross, Feb 04 2008 STATUS approved

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Last modified September 20 18:52 EDT 2019. Contains 327245 sequences. (Running on oeis4.)