

A027861


Numbers k such that k^2 + (k+1)^2 is prime.


38



1, 2, 4, 5, 7, 9, 12, 14, 17, 19, 22, 24, 25, 29, 30, 32, 34, 35, 39, 42, 47, 50, 60, 65, 69, 70, 72, 79, 82, 84, 85, 87, 90, 97, 99, 100, 102, 104, 109, 110, 115, 122, 130, 135, 137, 139, 144, 149, 154, 157, 160, 162, 164, 167, 172, 174, 185, 187, 189, 195, 199, 202
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OFFSET

1,2


COMMENTS

k > 1 never ends in 1, 3, 6 or 8, (that is, k*(k+1) does not end in 2).  Lekraj Beedassy, Jul 09 2004
k can never be congruent to (1 or 3) mod 5, because if it were, then k^2 + (k+1)^2 would be divisible by 5. In other words, for k > 1, this sequence cannot contain any values in A047219. This means that we can immediately discard 40% of all possible k.  Dmitry Kamenetsky, Sep 02 2008


LINKS

T. D. Noe and Zak Seidov, Table of n, a(n) for n = 1..10000
Patrick De Geest, World!Of Numbers


FORMULA

a(n) = (1/2)*(sqrt(2*A027862(n)1)1).  Zak Seidov, Jul 22 2013
A010051(A001844(a(n))) = 1.  Reinhard Zumkeller, Jul 13 2014


MATHEMATICA

Select[Range[250], PrimeQ[#^2+(#+1)^2]&] (* Harvey P. Dale, Dec 31 2017 *)


PROG

(MAGMA) [n: n in [0..1000] IsPrime(n^2 + (n+1)^2)]; // Vincenzo Librandi, Nov 19 2010
(Haskell)
a027861 n = a027861_list !! (n1)
a027861_list = filter ((== 1) . a010051 . a001844) [0..]
 Reinhard Zumkeller, Jul 13 2014
(PARI) is(n)=isprime(n^2 + (n+1)^2) \\ Charles R Greathouse IV, Apr 28 2015


CROSSREFS

Complement of A012132.
Equals (A002731(n+1)1)/2. A027862 gives primes, A091277 gives prime index.
Cf. A047219, A001844, A010051.
Sequence in context: A286753 A325543 A214051 * A219648 A062428 A250000
Adjacent sequences: A027858 A027859 A027860 * A027862 A027863 A027864


KEYWORD

nonn,easy


AUTHOR

Patrick De Geest


STATUS

approved



