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A212821 Smallest prime p of the form p = 3^n + k, where k has n prime divisors counted with multiplicity. 0

%I #23 Jun 27 2014 13:10:20

%S 2,5,13,47,97,419,953,3019,7457,20963,61609,189947,557041,1614803,

%T 4840313,14430827,43276097,129959363,388862281,1165669339,3493338001,

%U 10471887539,31395739673

%N Smallest prime p of the form p = 3^n + k, where k has n prime divisors counted with multiplicity.

%e a(0) = 2 because 2 = 1 (A001222(1) = 0) + 3^0 = 1 + 1;

%e a(1) = 5 because 5 = 2 (A001222(2) = 1) + 3^1 = 2 + 3;

%e a(2) = 13 because 13 = 4 (A001222(4) = 2) + 3^2 = 4 + 9;

%e a(3) = 47 because 47 = 20 (A001222(20) = 3) + 3^3 = 20 + 27;

%e a(4) = 97 because 97 = 16 (A001222(16) = 4) + 3^4 = 16 + 81;

%e a(5) = 419 because 419 = 176 (A001222(176) = 5) + 3^5 = 176 + 243.

%o (PARI) for(n=0, 30, p=3^n; k=1; while(1, if(bigomega(k)==n && isprime(p+k), print1(p+k, ", "); break, k++))) \\ _Colin Barker_, Jun 27 2014

%Y Cf. A001222.

%K nonn

%O 0,1

%A _Juri-Stepan Gerasimov_, Jul 02 2012

%E More terms from _Colin Barker_, Jun 27 2014

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)