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%I #75 Mar 11 2022 08:34:17
%S 17,53,71,89,107,179,197,233,251,269,359,431,449,467,503,521,557,593,
%T 647,683,701,719,773,809,827,863,881,953,971,1061,1097,1151,1187,1223,
%U 1259,1277,1367,1439,1493,1511,1583,1601,1619,1637,1709,1871,1889,1907
%N Primes of the form 9*k - 1.
%C Or, primes of the form 18k - 1. Corresponding values of k are in A138918. - _Zak Seidov_, Apr 03 2008
%C From _Doug Bell_, Mar 23 2009: (Start)
%C Conjecture: if a(n) = 9x - 1, 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.
%C Example: x = 2, a(n) = 17: 2/17 = 0.1176470588235294... repeating with a cycle of 16.
%C 1176470588235294 * 3/2 = 1764705882352941, which is 1176470588235294 rotated to the left.
%C 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)
%C The last conjecture is false. For example, for x = 3 we have 230769*(4/3) = 307692, but 9*3-1 = 26 is not in the sequence. - _Giovanni Resta_, Jul 28 2015
%C Conjecture: Primes p such that ((x+1)^9-1)/x has 4 irreducible factors of degree 2 over GF(p). - _Federico Provvedi_, Jun 27 2018
%H Harry J. Smith, <a href="/A061242/b061242.txt">Table of n, a(n) for n = 1..1000</a>
%F A010888(a(n)) = 8. - _Reinhard Zumkeller_, Feb 25 2005
%p select(isprime, [seq(18*i-1,i=1..1000)]); # _Robert Israel_, Sep 03 2014
%t Select[ Range[ 2500 ], PrimeQ[ # ] && Mod[ #, 9 ] == 8 & ]
%t Select[9*Range[300] - 1, PrimeQ]
%o (Python)
%o from sympy import prime
%o A061242 = [p for p in (prime(n) for n in range(1,10**3)) if not (p+1) % 18]
%o # _Chai Wah Wu_, Sep 02 2014
%o (Magma) [a: n in [0..250] | IsPrime(a) where a is 9*n - 1 ]; // _Vincenzo Librandi_, Jun 07 2015
%o (PARI) select( {is(n)=n%9==8&&isprime(n)}, primes([1,2000])) \\ _M. F. Hasler_, Mar 10 2022
%Y Cf. A061237, A061238, A061239, A061240, A061241 (p mod 9 = 1, 2, 4, 5 and 7), A138918 (18n - 1 is prime), A258663 (9n - 1 is prime).
%Y Can be partitioned in disjoint subsequences A062343 (primes with sum of digits s = 8), A106758 (s = 17), A106764 (s = 26), A106770 (s = 35), A106776 (s = 44), A106782 (s = 53), A107617 (s = 62), etc.
%K nonn,easy
%O 1,1
%A _Amarnath Murthy_, Apr 23 2001
%E More terms from _Robert G. Wilson v_, May 10 2001
%E Edited by _N. J. A. Sloane_ at the suggestion of _R. J. Mathar_, Apr 30 2008
%E Edited by _M. F. Hasler_, Mar 10 2022
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