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

7, 11, 29, 17, 19, 23, 53, 29, 31, 103, 191, 41, 43, 47, 73, 101, 53, 109, 59, 311, 97, 67, 103, 71, 149, 191, 79, 83, 173, 89, 181, 283, 97, 197, 101, 103, 107, 109, 331, 113, 229, 709, 367, 311, 127, 193, 131, 269, 137, 139, 569, 293, 149, 151, 229, 463

Offset: 1

Author

Ahmad J. Masad, Nov 15 2020

Keywords

• nonn

Comments

In A002808(n)-base numeral system, a(n) is the smallest prime number for which the digital root is 1.

Conjecture: As n approaches infinity, the probability that a prime number is a term in this sequence approaches 1.

Conjecture: There are infinitely many primes that are not terms in this sequence.

The sequence for all positive numbers (instead of A072668) is A034694. - Peter Munn, May 02 2023

Examples

			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.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002808, A034694, A072668, A339540.

Programs

Mathematica

Map[Block[{p = NextPrime[#]}, While[Mod[p, #] != 1, p = NextPrime[p]]; p] &, Select[Range[4, 78], CompositeQ] - 1] (* Michael De Vlieger, Dec 10 2020 *)

PARI

f(x) = {my(p=nextprime(x)); while ((p % x) != 1, p = nextprime(p+1)); p;}
lista(nn) = {my(list = List()); forcomposite(c=1, nn, listput(list, f(c-1));); Vec(list);} \\ Michel Marcus, Nov 17 2020

Extensions

More terms from Michel Marcus, Nov 17 2020