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

Author

W. Edwin Clark Nov 06 2003

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

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

Crossrefs

Cf. A089294.

Extensions

More terms from David Wasserman, Aug 31 2005