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A273372 Squares ending in digit 1. 3
1, 81, 121, 361, 441, 841, 961, 1521, 1681, 2401, 2601, 3481, 3721, 4761, 5041, 6241, 6561, 7921, 8281, 9801, 10201, 11881, 12321, 14161, 14641, 16641, 17161, 19321, 19881, 22201, 22801, 25281, 25921, 28561, 29241, 32041, 32761, 35721, 36481, 39601, 40401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Intersection of A000290 and A017281; also, union of A017282 and A017378. The square roots are in A017281 or in A017377 (numbers ending in 1 or 9, respectively). - David A. Corneth, May 22 2016

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

G.f.: x*(1 + 80*x + 38*x^2 + 80*x^3 + x^4) / ((1 + x)^2*(1 - x)^3).

a(n) = 10*A132356(n-1) + 1 = 5*(10*n+(-1)^n-5)*(2*n+(-1)^n-1)/4+1.

a(n) = (5*n - 5/2 + (3/2)*(-1)^n)^2 = 25*n^2 - 25*n + 17/2 + 15*n*(-1)^n - (15/2)*(-1)^n. - David A. Corneth, May 21 2016

a(n) = A090771(n)^2. - Michel Marcus, May 25 2016

MATHEMATICA

Table[5 (10 n + (-1)^n - 5) (2 n + (-1)^n - 1)/4 + 1, {n, 1, 50}]

PROG

(Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 1];

(Magma) [5*(10*n+(-1)^n-5)*(2*n+(-1)^n-1)/4+1: n in [1..50]];

(Ruby) p (1..(n + 1) / 2).inject([]){|s, i| s + [(10 * i - 9) ** 2, (10 * i - 1) ** 2]}[0..n - 1] # Seiichi Manyama, May 24 2016

(Python)

A273372_list = [(10*n+m)**2 for n in range(10**3) for m in (1, 9)] # Chai Wah Wu, May 24 2016

CROSSREFS

Cf. A000290, A090771, A132356.

Cf. A017281 (numbers ending in 1), A017283 (cubes ending in 1).

Cf. similar sequences listed in A273373.

Sequence in context: A357168 A253261 A280587 * A053887 A119943 A001245

Adjacent sequences:  A273369 A273370 A273371 * A273373 A273374 A273375

KEYWORD

nonn,base,easy

AUTHOR

Vincenzo Librandi, May 21 2016

EXTENSIONS

Edited by Bruno Berselli, May 24 2016

STATUS

approved

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Last modified September 30 01:05 EDT 2022. Contains 357092 sequences. (Running on oeis4.)