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A213011 Union of positive squares and sums of first k primes. 0
1, 2, 4, 5, 9, 10, 16, 17, 25, 28, 36, 41, 49, 58, 64, 77, 81, 100, 121, 129, 144, 160, 169, 196, 197, 225, 238, 256, 281, 289, 324, 328, 361, 381, 400, 440, 441, 484, 501, 529, 568, 576, 625, 639, 676, 712, 729, 784, 791, 841, 874, 900, 961, 963, 1024, 1060, 1089, 1156, 1161, 1225, 1264, 1296, 1369, 1371, 1444, 1480, 1521, 1593, 1600, 1681, 1720, 1764 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If S_k denotes sum of the first k primes (A007504(n)), there is a square strictly between S_k and S_{k+1} for all k.

REFERENCES

R. Honsberger, Problem 88, The Sums of the Primes, Mathematical Morsels, MAA, 1978, pp. 221-222.

LINKS

Table of n, a(n) for n=1..72.

CROSSREFS

Union of A000290 and A007504.

Sequence in context: A282737 A039891 A280729 * A175265 A320225 A070924

Adjacent sequences: A213008 A213009 A213010 * A213012 A213013 A213014

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 01 2012

STATUS

approved

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)