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A089297
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Maximum prime required in the representation of the square of the n-th prime A000040(n) by a signed sum of squares of distinct other primes minimizing the number of terms in the sum.
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2
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29, 37, 19, 19, 19, 31, 19, 17, 19, 23, 29, 31, 31, 37, 37, 47, 43, 47, 53, 59, 59, 59, 71, 67, 71, 73, 79, 79, 83, 83, 97, 97, 101, 101, 109, 109, 127, 127, 127, 137, 139, 131, 149, 139, 151, 149, 163, 167, 191, 173, 167, 179, 179, 191, 191, 193, 193, 193, 199, 211
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(1) requires 6 squares, a(2) requires 8, a(3) requires 5 and a(4) through a(70) require 3. - David Wasserman (wasserma(AT)spawar.navy.mil), Sep 01 2005
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LINKS
| T. Lassila, H. Pfoertner et al., Sum of unique prime squares? Thread in NG sci.math, Oct 21 2003.
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EXAMPLE
| The first representations different from those in A089296 are
a(6)=31: 13^2 = 169 = 31^2 - 29^2 + 7^2 = -31^2 + 29^2 + 17^2
a(10)=23: 29^2 = 841 = 23^2 + 19^2 - 7^2
a(11)=29: 31^2 = 961 = 29^2 + 13^2 - 7^2
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CROSSREFS
| Cf. A088934 representation of n by distinct squares of primes, A089296 representation of (n-th prime)^2 with maximum term minimized.
Sequence in context: A172413 A134254 A089296 * A127956 A166088 A172195
Adjacent sequences: A089294 A089295 A089296 * A089298 A089299 A089300
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 18 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 01 2005
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