A062875 -id:A062875 - cp's OEIS frontend

A062876 Numbers of lattice points corresponding to incrementally largest circle radii in A062875.

4, 12, 20, 28, 44, 52, 68, 76, 92, 116, 124, 148, 164, 172, 188, 212, 236, 244, 268, 284, 292, 316, 332, 356, 388, 404, 412, 428, 436, 452, 508, 524, 548, 556, 596, 604, 628, 652, 668, 692, 716, 724, 764, 772, 788, 796, 844, 892, 908, 916, 932, 956, 964

Offset: 1

Eric W. Weisstein

For n = 1 and n >= 3, a(n) is the smallest nonsquarefree number divisible by prime(n). - David James Sycamore, Jun 15 2024

Ray Chandler, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Circle Lattice Points

Cf. A046112, A062875.
Cf. A017113, A111333.
Cf. A000040, A103929

[4] cat [4*NthPrime(n): n in [2..60]]; // Vincenzo Librandi, May 08 2015

Join[{4}, Table[4 Prime[n], {n, 2, 50}]] (* Vincenzo Librandi, May 08 2015 *)

a(n)=if(n>1,4*prime(n),4) \\ Charles R Greathouse IV, May 08 2015

from sympy import prime
def A062876(n): return prime(n)<<2 if n>1 else 4 # Chai Wah Wu, Aug 02 2024

a(n) = A017113(A111333(n)-1) = 8*A111333(n) - 4.

For n >= 2 a(n) = 4*A000040(n) (a term in A013929). - David James Sycamore, Jun 15 2024

Edited and extended by Ray Chandler, Jan 05 2012

A111333 Number of odd numbers <= n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 16, 19, 21, 22, 24, 27, 30, 31, 34, 36, 37, 40, 42, 45, 49, 51, 52, 54, 55, 57, 64, 66, 69, 70, 75, 76, 79, 82, 84, 87, 90, 91, 96, 97, 99, 100, 106, 112, 114, 115, 117, 120, 121, 126, 129, 132, 135, 136, 139, 141, 142, 147, 154, 156, 157

Offset: 1

Giovanni Teofilatto, Nov 05 2005

This is A006254 (numbers n such that 2n-1 is prime) with a leading 1. - Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 06 2005
Same as smallest k such that prime(n) divides C(2k,k). - Jonathan Sondow, Jan 20 2016
Positions of records in A046112. - Hugo Pfoertner, Jul 11 2019

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A006254, A046112, A049990, A062875.

seq(ceil(ithprime(i)/2), i=1..100); # Robert Israel, Jan 20 2016

Table[ Ceiling[ Prime[n]/2], {n, 65}] (* Robert G. Wilson v, Nov 07 2005 *)

a(n)=(prime(n)+1)\2 \\ Charles R Greathouse IV, Sep 16 2015

from sympy import prime
def A111333(n): return prime(n)+1>>1 # Chai Wah Wu, Aug 02 2024

a(n) = ceiling((prime_n)/2). - Robert G. Wilson v, Nov 07 2005

More terms from Robert G. Wilson v, Nov 07 2005

cp's OEIS Frontend

A062876 Numbers of lattice points corresponding to incrementally largest circle radii in A062875.

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