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Numbers n such that the distance from n to the next prime is the same as the distance from n^2 to the next prime.
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%I #20 Jun 14 2013 01:02:01

%S 1,2,3,4,6,7,8,9,10,13,15,16,21,31,36,37,38,39,40,45,48,50,57,61,64,

%T 66,67,76,81,85,91,97,99,103,105,111,126,130,131,141,147,150,151,154,

%U 156,163,168,171,180,181,185,193,202,207,210,216,225,235,237,240,246,248,249,250,253

%N Numbers n such that the distance from n to the next prime is the same as the distance from n^2 to the next prime.

%C Numbers n such that (smallest prime > n)- n = (smallest prime > n^2)- n^2.

%C Primes in the sequence are: 2, 3, 7, 13, 31, 37, 61, 67, 97, 103, 131, 151, 163, 181, 193,...

%H Charles R Greathouse IV, <a href="/A226381/b226381.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A013632(n) = A013632(n^2)}. - _R. J. Mathar_, Jun 09 2013

%e 1 is in the sequence because the distance from 1 to 2 is the same as the distance from 1^2 to 2.

%e 2 is in the sequence because the distance from 2 to 3 is the same as the distance from 2^2 to 5.

%e 3 is in the sequence because the distance from 3 to 5 is the same as the distance from 3^2 to 11.

%t Select[Range[235], NextPrime[#] - # == NextPrime[#^2] - #^2 &] (* _Giovanni Resta_, Jun 09 2013 *)

%o (PARI) is(n)=nextprime(n+1)-n==nextprime(n^2)-n^2 \\ _Charles R Greathouse IV_, Jun 14 2013

%K nonn

%O 1,2

%A _Gerasimov Sergey_, Jun 05 2013

%E Corrected by _Giovanni Resta_, Jun 09 2013