A004232 a(n) = n^2 + prime(n).

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

Offset: 1

Author

wild(AT)edumath.u-strasbg.fr (Daniel Wild)

Keywords

• nonn
• easy

Comments

Sum of reciprocals = 0.766167481.... - Cino Hilliard, 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 < 10^10 (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

Crossrefs

Cf. A184935.

Programs

Magma

[n^2 +NthPrime(n): n in [1..250]]; // Vincenzo Librandi, Apr 14 2011

Mathematica

Table[n^2+Prime[n],{n,50}] (* Harvey P. Dale, Feb 28 2015 *)

PARI

primeppwr(n) = sr=0; for(x=1,n, y=x^2+prime(x); print1(y","); sr+=1./y; ); print(); print(sr) \\ Cino Hilliard

Extensions

More terms from Cino Hilliard, Dec 31 2003