

A111043


Partial sums of squares of digits of golden ratio phi.


1



1, 37, 38, 102, 102, 111, 120, 201, 265, 329, 378, 394, 475, 539, 620, 636, 700, 716, 780, 784, 784, 800, 825, 889, 925, 989, 998, 1014, 1023, 1059, 1084, 1120, 1129, 1193, 1194, 1195, 1244, 1293, 1297, 1297, 1306, 1306, 1387, 1388, 1437, 1518, 1582, 1582
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OFFSET

1,2


COMMENTS

a(n) is prime for n = 2, 33, 34, 39, 40, 49, ...
a(n) is semiprime for n = 3, 6, 8, 9, 10, 12, 24, 26, 27, 30, 36, 38, 41, 43, 45, ...
a(n) is a perfect power for n = 20, 21, ...


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = sum(i=1 to n) A001622(i)^2.


EXAMPLE

a(1) = 1^2 = 1,
a(2) = 1^2 + 6^2 = 37, which is prime,
a(3) = 1^2 + 6^2 + 1^2 = 38,
a(4) = 1^2 + 6^2 + 1^2 + 8^2 = 102.


MATHEMATICA

Accumulate[RealDigits[GoldenRatio, 10, 120][[1]]^2] (* Harvey P. Dale, Jul 22 2014 *)


CROSSREFS

Cf. A001622, A111033, A111034.
Sequence in context: A296871 A071887 A168143 * A041683 A064172 A242989
Adjacent sequences: A111040 A111041 A111042 * A111044 A111045 A111046


KEYWORD

base,easy,nonn


AUTHOR

Jonathan Vos Post, Oct 06 2005


EXTENSIONS

Definition clarified by Harvey P. Dale, Jul 22 2014


STATUS

approved



