A129592 The smallest in a triple of three consecutive primes such that the ceiling of the square root of their sums-of-squares is prime.

2, 7, 13, 43, 53, 59, 127, 241, 271, 317, 331, 349, 367, 439, 487, 491, 607, 659, 719, 733, 757, 773, 821, 857, 881, 929, 971, 1087, 1193, 1259, 1289, 1303, 1409, 1427, 1453, 1607, 1663, 1693, 1723, 1747, 1789, 1949, 2053, 2087, 2089, 2131, 2251, 2333, 2393, 2467, 2549, 2633, 2671, 2719

Offset

1,1

Comments

Can three squares with consecutive prime sides prime(i), i=k,...,k+2, be contained/morphed in a larger square also with prime sides just slightly greater than required?

The areas are the squares of the prime sides; the total area is their sum prime(k)^2 + prime(k+1)^2 + prime(k+2)^2, and pulling the square root is the diagonal of the hosting square. The sequence lists the first, prime(k), if this diagonal (rounded up) is a prime number, indicating that a rather tight enclosing square with (again) a prime side length can be found.

Links

Table of n, a(n) for n=1..54.

Formula

{A000040(n): ceiling(sqrt(A133529(n))) in A000040}. - R. J. Mathar, Jul 10 2011

Example

Take 13,17,19 with summed squares 169 + 289 + 361 = 819 = A133529(6). The square root is approximately 28.6 and rounding up to 29 yields a prime, so 13 is a term.

Mathematica

Select[Partition[Prime[Range[400]], 3, 1], PrimeQ[Ceiling[ Sqrt[ Total[ #^2]]]]&][[All, 1]] (* Harvey P. Dale, Feb 05 2019 *)

Crossrefs

Sequence in context: A217305 A026555 A262727 * A153136 A178607 A321407

Adjacent sequences: A129589 A129590 A129591 * A129593 A129594 A129595

Keyword

nonn

Author

J. M. Bergot, May 30 2007

Extensions

Edited and extended by R. J. Mathar, Jul 10 2011

Status

approved