

A216898


a(n) = smallest number k such that both k  n^2 and k + n^2 are primes.


2



2, 4, 7, 14, 21, 28, 43, 52, 67, 86, 111, 150, 149, 180, 201, 232, 267, 312, 329, 366, 411, 446, 487, 532, 587, 654, 705, 742, 787, 852, 911, 972, 1029, 1118, 1185, 1242, 1313, 1372, 1473, 1528, 1603, 1692, 1769, 1852, 1941, 2032, 2127, 2212, 2317, 2412, 2503
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OFFSET

0,1


COMMENTS

Note that a(11) = 150 and a(12) = 149. Up to n = 10^6, this is the only case where a(n) > a(n+1). What about general case of a(n) < a(n+1)?
First differences are almost linear with n hence the only case with a(n) > a(n+1) is n = 11.  Zak Seidov, May 19 2014


LINKS

Zak Seidov, Table of n, a(n) for n = 0..10000


FORMULA

a(n) = A087711(n^2).  T. D. Noe, Sep 19 2012


EXAMPLE

a(11) = 150 because both 150  11^2 = 29 and 150 + 11^2 = 271 are primes.
a(12) = 149 because both 149  12^2 = 5 and 149 + 12^2 = 293 are primes.


MATHEMATICA

Table[If[n < 1, 2, m = n^2 + 1; While[!PrimeQ[m  n^2]  !PrimeQ[m + n^2], m = m + 2]; m], {n, 0, 100}]


CROSSREFS

Cf. A087711.
Sequence in context: A057264 A045514 A102957 * A176450 A263345 A181655
Adjacent sequences: A216895 A216896 A216897 * A216899 A216900 A216901


KEYWORD

nonn


AUTHOR

Zak Seidov, Sep 19 2012


STATUS

approved



