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

1,1

Comments

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, Aug 04 2006

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

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

Example

13 = 2^2 + 3^2.

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 *)

Crossrefs

Cf. A024450 (sum of squares of the first n primes).

Sequence in context: A098004 A257337 A056227 * A340771 A333848 A063606

Adjacent sequences: A048258 A048259 A048260 * A048262 A048263 A048264

Keyword

nonn

Author

Jud McCranie

Status

approved