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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 6 16:20 EDT 2021. Contains 343586 sequences. (Running on oeis4.)