Sum of Sequence of Squares of Primes
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Theorem
Let $S = \sequence {s_n}$ be the integer sequence defined as:
- $\ds s_n = \sum_{i \mathop = 1}^n {p_i}^2$
where $P_i$ denotes the $i$th prime number.
Then $S$ begins:
- $4, 13, 38, 87, 208, 377, 666, 1027, 1556, 2397, 3358, 4727, 6408, 8257, 10466, \ldots$
This sequence is A024450 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $666$