A111034 - OEIS

A111034

Sum of squares of digits of e.

4, 53, 54, 118, 122, 186, 187, 251, 255, 319, 335, 360, 441, 441, 457, 482, 486, 495, 520, 529, 565, 565, 569, 633, 682, 698, 747, 748, 757, 782, 786, 822, 858, 862, 878, 959, 1008, 1057, 1082, 1131, 1135, 1151, 1200, 1200, 1281, 1290, 1326, 1407, 1488, 1569

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OFFSET

1,1

COMMENTS

a(n) is prime for n = 2, 8, 15, 23, 29, ... a(n) is semiprime for n = 1, 4, 5, 7, 10, 11, 16, 21, 22, 24, 26, ... a(n) is a perfect power for n = 1, 13, 14, 20, ... Coincidentally, a(20) = 529 = 23^2 = sum of squares of first 18 digits of Pi.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n) = Sum_{i=1..n} A001113(i)^2.

EXAMPLE

a(1) = 2^2 = 4,

a(2) = 2^2 + 7^2 = 53, which is prime,

a(3) = 2^2 + 7^2 + 1^2 = 54,

a(4) = 2^2 + 7^2 + 1^2 + 8^2 = 118,

a(5) = 2^2 + 7^2 + 1^2 + 8^2 + 2^2 = 122.

MATHEMATICA

Accumulate[RealDigits[E, 10, 50][[1]]^2] (* Harvey P. Dale, Apr 05 2011 *)