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

1,1

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

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.

Example

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.

Mathematica

Select[Range[1, 1105, 4], PrimePowerQ[#] && Mod[FactorInteger[#][[1, 1]], 4] == 1 &] (* Oliver Seipel, Oct 13 2025 *)

Prog

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

Crossrefs

Disjoint union of A002144 and A146945.

Cf. A001844, subsequence of A000961.

Cf. A024409, subsequence of A008846.

Sequence in context: A004613 A008846 A162597 * A198440 A379985 A094194

Adjacent sequences: A120957 A120958 A120959 * A120961 A120962 A120963

Keyword

nonn

Author

Lekraj Beedassy, Jul 19 2006

Status

approved