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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)