A048261 Numbers that are the sum of the squares of distinct primes.
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
Offset: 1
Keywords
Examples
13 = 2^2 + 3^2.
References
- D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 17163.
Links
- T. D. Noe, Table of n, a(n) for n = 1..2000
- Robert E. Dressler, Louis Pigno, and Robert Young, Sums of squares of primes, Nordisk Mat. Tidskr. 24 (1976), 39-40. MR 54 #7373.
- Index entries for sequences related to sums of squares
Crossrefs
Cf. A024450 (sum of squares of the first n primes).
Programs
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Mathematica
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, Aug 04 2006 *)
Formula
It is easy to check that these 2438 numbers that 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. - W. Edwin Clark, Oct 19 2003
Comments