A089294 -id:A089294 - cp's OEIS frontend

A089295 Positions of the records in A089294. First integer requiring a larger prime in its representation by (signed) sums of squares of distinct primes than all preceding integers.

0, 643, 1172, 2013, 2974, 4343, 6024, 7873, 10082, 12891, 16372, 20093, 24582, 29623, 34952, 41193, 48082, 56003, 65412, 75613, 86222, 97671, 109552, 122321, 138450, 155611, 174380, 193701, 215902, 238703, 263352, 289921, 317810, 347739

Offset: 1

W. Edwin Clark Nov 06 2003

nonn

a(2)=643 was first given by Robert Israel.

			a(1)=0=19^2-17^2-11^2+7^2 (0 already requires 19)
a(2)=643=23^2+19^2-13^2-7^2-5^2-2^2 (requires 23)
a(3)=1172=29^2+23^2-13^2-5^2-2^2
a(4)=2013=31^2+29^2+17^2-7^2-5^2-2^2
a(5)=2974=37^2+29^2+23^2+17^2-7^2-3^2+2^2=37^2+31^2+23^2+13^2-7^2-3^2+2^2
(two representations with the same maximum term)

Robert B. Israel, Sum of unique prime squares? Posting in NG sci.math.

Cf. A089294.

More terms from David Wasserman, Aug 31 2005

A088934 Maximum prime required for the representation of n by a signed sum of squares of distinct primes that has the minimal number of terms A088910(n).

Original entry on oeis.org

19, 13, 19, 13, 2, 3, 13, 19, 13, 3, 13, 7, 5, 3, 13, 7, 5, 13, 13, 7, 5, 5, 19, 13, 7, 5, 13, 13, 7, 5, 5, 19, 13, 7, 5, 13, 7, 7, 5, 13, 7, 17, 11, 11, 7, 7, 17, 11, 13, 7, 17, 11, 13, 7, 7, 17, 11, 13, 7, 11, 11, 7, 7, 11, 13, 7, 17, 11, 11, 7, 7, 17, 11, 13, 7, 17, 11, 11, 7, 7, 17, 11

Offset: 0

Hugo Pfoertner, Nov 06 2003

nonn

			See example in A088910.

Cf. A089294 representation minimizing the maximum occurring prime instead of minimizing the number of terms, A089297 representation of the squares of primes by squares of distinct other primes.

A089296 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 largest prime used in the sum.

Original entry on oeis.org

29, 37, 19, 19, 19, 19, 19, 17, 19, 19, 19, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 43, 43, 47, 47, 53, 53, 53, 53, 59, 61, 61, 61, 67, 67, 67, 71, 71, 71, 73, 73, 79, 79, 79, 79, 83, 89, 89, 89, 89, 97, 97, 97, 101, 101, 101, 101, 103, 103, 103, 103, 107, 107, 109

Offset: 1

Hugo Pfoertner, Nov 18 2003

nonn

			a(1)=29: 2^2 = 4 = -29^2 + 19^2 + 17^2 + 11^2 + 7^2 + 5^2
a(2)=37: 3^2 = 9 = -37^2 + 23^2 + 19^2 + 17^2 + 11^2 + 7^2 + 5^2 + 2^2
a(3)=19: 5^2 = 25 = -19^2 + 17^2 + 13^2 - 11^2 + 7^2
a(4)=19: 7^2 = 49 = -19^2 + 17^2 + 11^2

T. Lassila, H. Pfoertner et al., Sum of unique prime squares? Thread in NG sci.math, Oct 21 2003.

Cf. A089294 representation of n by distinct squares of primes, A089297 representation of (n-th prime)^2 with minimal number of terms.

More terms from David Wasserman, Sep 01 2005

cp's OEIS Frontend

A089295 Positions of the records in A089294. First integer requiring a larger prime in its representation by (signed) sums of squares of distinct primes than all preceding integers.

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A088934 Maximum prime required for the representation of n by a signed sum of squares of distinct primes that has the minimal number of terms A088910(n).

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Author

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Examples

Crossrefs

A089296 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 largest prime used in the sum.

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Author

Keywords

Examples

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