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A061101 Squares with digital root 7. 1
16, 25, 169, 196, 484, 529, 961, 1024, 1600, 1681, 2401, 2500, 3364, 3481, 4489, 4624, 5776, 5929, 7225, 7396, 8836, 9025, 10609, 10816, 12544, 12769, 14641, 14884, 16900, 17161, 19321, 19600, 21904, 22201, 24649, 24964, 27556, 27889, 30625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Amarnath Murthy & Charles Ashbacher, Fabricating a perfect square with a given valid digit sum, in Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences, pp 154-156.

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

FORMULA

Conjecture: a(n)=(9*n-8)^2/4 for n even. a(n)=(9*n-1)^2/4 for n odd. G.f.: x*(16+9*x+112*x^2+9*x^3+16*x^4)/((1-x)^3*(1+x)^2). - Colin Barker, Apr 21 2012

Conjecture is true, because x^2 == 7 (mod 9) if and only if x == 4 or 5 (mod 9). - Robert Israel, Jan 31 2017

EXAMPLE

1681=41^2, 1+6+8+1 = 16, 1+6 =7, 4624=68^2, 4+6+2+4 = 16, 1+6 =7.

MAPLE

seq(seq((9*i+j)^2, j=4..5), i=0..100); # Robert Israel, Jan 31 2017

PROG

(PARI) b=0; for (n=1, 1000, until (s==7, b++; s=b^2; s-=9*(s\9)); write("b061101.txt", n, " ", b^2)) \\ Harry J. Smith, Jul 18 2009

(PARI) a(n)=(n\2*9-4*(-1)^n)^2 \\ Charles R Greathouse IV, Sep 21 2012

CROSSREFS

Cf. A056991.

Sequence in context: A188826 A152152 A260047 * A166672 A167358 A267764

Adjacent sequences:  A061098 A061099 A061100 * A061102 A061103 A061104

KEYWORD

nonn,base,easy

AUTHOR

Amarnath Murthy, Apr 19 2001

EXTENSIONS

More terms from Harry J. Smith, Jul 18 2009

STATUS

approved

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Last modified April 20 07:46 EDT 2021. Contains 343125 sequences. (Running on oeis4.)