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A070155 Numbers n such that n-1, n+1 and 1+n^2 are prime numbers. 9
4, 6, 150, 180, 240, 270, 420, 570, 1290, 1320, 2310, 2550, 2730, 3360, 3390, 4260, 4650, 5850, 5880, 6360, 6780, 9000, 9240, 9630, 10530, 10890, 11970, 13680, 13830, 14010, 14550, 16230, 16650, 18060, 18120, 18540, 19140, 19380, 21600, 21840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Essentially the same as A129293. - R. J. Mathar, Jun 14 2008

Solutions to the equation: A000005(n^4-1) = 8. - Enrique Pérez Herrero, May 03 2012

Terms > 6 are multiples of 30. Subsequence of A070689. - Zak Seidov, Nov 12 2012

{a(n)-1} is a subsequence of A157468; for n>1, {a(n)^2+2} is a subsequence of A242720. - Vladimir Shevelev, Aug 31 2014

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

For n>1, a(n)^2 = A242720(pi(a(n)-2)) - 2, where pi(n) is the prime counting function (A000720). - Vladimir Shevelev, Sep 02 2014

EXAMPLE

n=150: 149,151 and 22501 are all primes

MAPLE

select(n -> isprime(n-1) and isprime(n+1) and isprime(n^2+1), [seq(2*i, i=1..10000)]); # Robert Israel, Sep 02 2014

MATHEMATICA

Do[s=n; If[PrimeQ[s-1]&&PrimeQ[s+1]&&PrimeQ[1+s^2], Print[n]], {n, 1, 1000000}]

Select[Range[22000], AllTrue[{#+1, #-1, #^2+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 19 2014 *)

CROSSREFS

Cf. A001359, A006512, A014574, A002496, A005574, A070156, A070689.

Sequence in context: A052672 A137025 A176493 * A280778 A197882 A074124

Adjacent sequences:  A070152 A070153 A070154 * A070156 A070157 A070158

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, Apr 23 2002

STATUS

approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)