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Smallest prime p congruent to 1 modulo prime(10^n).
1

%I #14 Apr 30 2024 01:47:57

%S 3,59,9739,63353,209459,15596509,154858631,1794246731,4076149487,

%T 45603526979,11092303227413,93864728285579,1319833868136653,

%U 11656098322067917,27803086068196217,1781976386163140977,32382366940106296979,100447117955224696057,707388643757314709297

%N Smallest prime p congruent to 1 modulo prime(10^n).

%H Amiram Eldar, <a href="/A215609/b215609.txt">Table of n, a(n) for n = 0..24</a>

%F a(n) = A035095(10^n).

%e a(0) = 3 because p = prime(1) = 2, 3 = 1+p.

%e a(1) = 59 because p = prime(10) = 29, 59 = 1+2*p.

%e a(2) = 9739 because p = prime(10) = 29, 59 = 1+18*p.

%t a[n_]:=(If[n<2,3,p=Prime[n];r=2p+1;While[!PrimeQ[r],r=r+2p];r]);Table[a[10^n],{n,0,12}]

%Y Cf. A035095, A006988.

%K nonn

%O 0,1

%A _Zak Seidov_, Aug 17 2012

%E a(13)-a(18) from _Amiram Eldar_, Apr 30 2024