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A004232
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n^2 + prime(n).
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3
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3, 7, 14, 23, 36, 49, 66, 83, 104, 129, 152, 181, 210, 239, 272, 309, 348, 385, 428, 471, 514, 563, 612, 665, 722, 777, 832, 891, 950, 1013, 1088, 1155, 1226, 1295, 1374, 1447, 1526, 1607, 1688, 1773, 1860, 1945, 2040, 2129, 2222, 2315, 2420, 2527, 2628, 2729
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sum of reciprocals = 0.766167481.. - Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2003
The subset of primes begins: 3, 7, 23, 83, 181, 239, 563, 1013, 1447, 1607, 2129, 2729 = A184935. The subset of squares begins: 36, 49, no more through n = 100 [Jonathan Vos Post, Feb 02, 2011].
No more squares using primes < 1e10 (n ~ 45 million). The naive heuristic (not really applicable here, but it's a starting point) suggests something like sqrt(log(x)) up to x. [Charles R Greathouse IV, Feb 06 2011]
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PROG
| (PARI) primeppwr(n) = { sr=0; for(x=1, n, y=x^2+prime(x); print1(y", "); sr+=1./y; ); print(); print(sr) } (Cino Hilliard)
(MAGMA) [n^2 +NthPrime(n): n in [1..250]]; // Vincenzo Librandi, Apr 14 2011
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CROSSREFS
| Cf. A184935.
Sequence in context: A146931 A176675 A115285 * A140462 A093523 A173247
Adjacent sequences: A004229 A004230 A004231 * A004233 A004234 A004235
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KEYWORD
| nonn,easy
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AUTHOR
| wild(AT)edumath.u-strasbg.fr (Daniel Wild)
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EXTENSIONS
| More terms from Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2003
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