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A338929 a(n) is the smallest prime number p larger than A072668(n) such that p is equal to 1 (mod A072668(n)).

%I A338929 #46 May 03 2023 09:14:27
%S A338929 7,11,29,17,19,23,53,29,31,103,191,41,43,47,73,101,53,109,59,311,97,
%T A338929 67,103,71,149,191,79,83,173,89,181,283,97,197,101,103,107,109,331,
%U A338929 113,229,709,367,311,127,193,131,269,137,139,569,293,149,151,229,463
%N A338929 a(n) is the smallest prime number p larger than A072668(n) such that p is equal to 1 (mod A072668(n)).
%C A338929 In A002808(n)-base numeral system, a(n) is the smallest prime number for which the digital root is 1.
%C A338929 Conjecture: As n approaches infinity, the probability that a prime number is a term in this sequence approaches 1.
%C A338929 Conjecture: There are infinitely many primes that are not terms in this sequence.
%C A338929 The sequence for all positive numbers (instead of A072668) is A034694. - _Peter Munn_, May 02 2023
%H A338929 Michel Marcus, <a href="/A338929/b338929.txt">Table of n, a(n) for n = 1..10000</a>
%e A338929 For n=20, A072668(20)=31, and 311 is the smallest prime number p larger than 31 such that p is equal to 1 (mod 31), so a(20)=311.
%t A338929 Map[Block[{p = NextPrime[#]}, While[Mod[p, #] != 1, p = NextPrime[p]]; p] &, Select[Range[4, 78], CompositeQ] - 1] (* _Michael De Vlieger_, Dec 10 2020 *)
%o A338929 (PARI)
%o A338929 f(x) = {my(p=nextprime(x)); while ((p % x) != 1, p = nextprime(p+1)); p;}
%o A338929 lista(nn) = {my(list = List()); forcomposite(c=1, nn, listput(list, f(c-1));); Vec(list);} \\ _Michel Marcus_, Nov 17 2020
%Y A338929 Cf. A000040, A002808, A034694, A072668, A339540.
%K A338929 nonn
%O A338929 1,1
%A A338929 _Ahmad J. Masad_, Nov 15 2020
%E A338929 More terms from _Michel Marcus_, Nov 17 2020