

A061242


Primes of the form 9*k  1.


15



17, 53, 71, 89, 107, 179, 197, 233, 251, 269, 359, 431, 449, 467, 503, 521, 557, 593, 647, 683, 701, 719, 773, 809, 827, 863, 881, 953, 971, 1061, 1097, 1151, 1187, 1223, 1259, 1277, 1367, 1439, 1493, 1511, 1583, 1601, 1619, 1637, 1709, 1871, 1889, 1907
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OFFSET

1,1


COMMENTS

Or, primes of the form 18i1. Corresponding values of i are in A138918.  Zak Seidov, Apr 03 2008
A010888(a(n)) = 8.  Reinhard Zumkeller, Feb 25 2005
From Doug Bell, Mar 23 2009: (Start)
It is my conjecture that if a(n) = 9x1, the integer formed by the repeating digits in the decimal fraction x/a(n) is the smallest integer such that rotating the digits to the left produces a number which is ((x+1)/x) times larger.
Example: x=2, a(n) = 17: 2/17 = 0.1176470588235294... repeating with a cycle of 16.
1176470588235294 x (3/2) = 1764705882352941, which is 1176470588235294 rotated to the left.
An additional conjecture is that the values of x from this sequence are the only values where rotating an integer one to the left produces a value (x+1)/x times as large. (End)
The last conjecture is false. For example, for x=3 we have 230769*(4/3)=307692, but 9*31 = 26 is not in the sequence.  Giovanni Resta, Jul 28 2015
Conjecture: Primes p such that ((x+1)^91)/x has 4 irreducible factors of degree 2 over GF(p).  Federico Provvedi, Jun 27 2018


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000


MAPLE

select(isprime, [seq(18*i1, i=1..1000)]); # Robert Israel, Sep 03 2014


MATHEMATICA

Select[ Range[ 2500 ], PrimeQ[ # ] && Mod[ #, 9 ] == 8 & ]
Select[9*Range[300]  1, PrimeQ]


PROG

(Python)
from sympy import prime
A061242 = [p for p in (prime(n) for n in range(1, 10**3)) if not (p+1) % 18]
# Chai Wah Wu, Sep 02 2014
(MAGMA) [a: n in [0..250]  IsPrime(a) where a is 9*n  1 ]; // Vincenzo Librandi, Jun 07 2015


CROSSREFS

Cf. A061237, A061238, A061239, A061240, A061241, A138918, A258663.
Sequence in context: A213997 A062342 A295869 * A062343 A176254 A287311
Adjacent sequences: A061239 A061240 A061241 * A061243 A061244 A061245


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, Apr 23 2001


EXTENSIONS

More terms from Robert G. Wilson v, May 10 2001
Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Apr 30 2008


STATUS

approved



