A120960 Pythagorean prime powers.

5, 13, 17, 25, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 125, 137, 149, 157, 169, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 289, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593

Offset: 1

Author

Lekraj Beedassy, Jul 19 2006

Keywords

• nonn

Comments

1 + sum of the indices of the first two numbers in A001844 that are divisible by n, if 1 + the sum of those indices equals n. - Mats Granvik, Oct 16 2007

R. J. Turyn proved [Baliga, et al., p. 129, gives the reference] that Williamson Hadamard matrices exist for 4t = 2(p^k + 1), for all primes p such that p == 1 (mod 4). - L. Edson Jeffery, Apr 10 2012

A024362(a(n)) = 1. - Reinhard Zumkeller, Dec 02 2012

Examples

			A001844(1) = 5 is divisible by 5, A001844(3) = 25 is divisible by = 5 and 1+3+1=5, so 5 is a member.
A001844(2) = 13 is divisible by = 13, A001844(10) = 221 is divisible by = 13 and 2+10+1=13 so 13 is a member.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
• A. Baliga and K. J. Horadam, Cocyclic Hadamard matrices over Z_t X Z^2_2, Australas. J. Combin. 11(1995), 123-134.
• Eric Weisstein's World of Mathematics, MathWorld, Centered Square Number.

Crossrefs

Cf. Disjoint union of A002144 and A146945.

Cf. A001844, subsequence of A000961.

Cf. A024409, subsequence of A008846.

Programs

Excel

Generate the indices with: =if(mod(1+2*row()*(row()+1);4*column()+1)=0;row();") Then sum the first two indices if it equals the column + 1. - Mats Granvik, Oct 16 2007

Haskell

import Data.List (elemIndices)
a120960 n = a120960_list !! (n-1)
a120960_list = map (+ 1) $ elemIndices 1 a024362_list
-- Reinhard Zumkeller, Dec 02 2012