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A102343 Numbers n such that n*10^3+777 is prime. 0


%S 1,2,11,19,22,26,41,43,44,47,50,53,65,67,68,71,76,79,80,83,94,97,107,

%T 110,113,115,122,124,125,131,134,136,137,145,146,152,155,158,167,169,

%U 170,173,176,181,184,199,202,211,212,226,229,232,233,250,253,254,268,272,274,281,284,286,292,295,298,299

%N Numbers n such that n*10^3+777 is prime.

%C The sequence is infinite, because by Dirichlet's theorem there are infinitely many primes in the arithmetic sequence A*n+B (n=1,2,...) if A an B are relatively prime. [Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009]

%C No term of the sequence is of form 3k, because the sum of digits of 10^3*3k+333=3*(10^3+259) is divisible by 3, violating the requirement of the definition. [Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009]

%e n=1: 1*10^3+777 = 1777 is prime, hence 1 is in the sequence.

%e n=50: 50*10^3+777 = 50777 is prime, hence 50 is in the sequence.

%e n=97: 97*10^3+777 = 97777 is prime, hence 97 is in the sequence.

%o (MAGMA) [ n: n in [0..300] | IsPrime(n*10^3+777) ];

%o (PARI) is(n)=isprime(n*10^3+777) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A157772, A102248, A159942. [Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009]

%K nonn,base,easy

%O 1,2

%A _Parthasarathy Nambi_, Feb 20 2005

%E Extended by Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009

%E Edited by R. J. Mathar, Apr 30 2009

%E More terms from _Vincenzo Librandi_, May 01 2009

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)