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Search: id:A048261
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| A048261 |
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Numbers that are the sum of the squares of distinct primes. |
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4
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| 4, 9, 13, 25, 29, 34, 38, 49, 53, 58, 62, 74, 78, 83, 87, 121, 125, 130, 134, 146, 150, 155, 159, 169, 170, 173, 174, 178, 179, 182, 183, 194, 195, 198, 199, 203, 204, 207, 208, 218, 222, 227, 231, 243, 247, 252, 256, 289, 290, 293, 294, 298, 299, 302, 303
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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17163 is the largest of 2438 positive integers that can't be expressed as the sum of squares of distinct primes. See A121518. - T. D. Noe (noe(AT)sspectra.com), Aug 04 2006
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REFERENCES
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Dressler, Robert E.; Pigno, Louis; and Young, Robert, Sums of squares of primes. Nordisk Mat. Tidskr. 24 (1976), no. 1, 39-40. MR 54 #7373.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 17163.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..2000
Index entries for sequences related to sums of squares
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FORMULA
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It is easy to check that these 2438 numbers which are not the sum of distinct primes squared are all of the form sum_i e_i*q_i where e_i is 1 or -1 and the q_i's are distinct primes. - Edwin Clark (eclark(AT)math.usf.edu), Oct 19, 2003
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EXAMPLE
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13 = 2^2 + 3^2.
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MATHEMATICA
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nn=10; s={0}; Do[p=Prime[n]; s=Union[s, s+p^2], {n, nn}]; s=Select[s, 0<#<=Prime[nn]^2&] - T. D. Noe (noe(AT)sspectra.com), Aug 04 2006
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CROSSREFS
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Cf. A024450 (sum of squares of the first n primes).
Sequence in context: A041905 A098004 A056227 this_sequence A063606 A033287 A041323
Adjacent sequences: A048258 A048259 A048260 this_sequence A048262 A048263 A048264
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net)
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