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A226381
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.
2
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, 66, 67, 76, 81, 85, 91, 97, 99, 103, 105, 111, 126, 130, 131, 141, 147, 150, 151, 154, 156, 163, 168, 171, 180, 181, 185, 193, 202, 207, 210, 216, 225, 235, 237, 240, 246, 248, 249, 250, 253
OFFSET
1,2
COMMENTS
Numbers n such that (smallest prime > n)- n = (smallest prime > n^2)- n^2.
Primes in the sequence are: 2, 3, 7, 13, 31, 37, 61, 67, 97, 103, 131, 151, 163, 181, 193,...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
{n: A013632(n) = A013632(n^2)}. - R. J. Mathar, Jun 09 2013
EXAMPLE
1 is in the sequence because the distance from 1 to 2 is the same as the distance from 1^2 to 2.
2 is in the sequence because the distance from 2 to 3 is the same as the distance from 2^2 to 5.
3 is in the sequence because the distance from 3 to 5 is the same as the distance from 3^2 to 11.
MATHEMATICA
Select[Range[235], NextPrime[#] - # == NextPrime[#^2] - #^2 &] (* Giovanni Resta, Jun 09 2013 *)
PROG
(PARI) is(n)=nextprime(n+1)-n==nextprime(n^2)-n^2 \\ Charles R Greathouse IV, Jun 14 2013
CROSSREFS
Sequence in context: A155763 A347350 A030319 * A180040 A166274 A376595
KEYWORD
nonn
AUTHOR
Gerasimov Sergey, Jun 05 2013
EXTENSIONS
Corrected by Giovanni Resta, Jun 09 2013
STATUS
approved