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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A045736 A158807 A377971 * A067006 A136020 A356467

Adjacent sequences: A338926 A338927 A338928 * A338930 A338931 A338932

Keyword

nonn

Author

Ahmad J. Masad, Nov 15 2020

Extensions

More terms from Michel Marcus, Nov 17 2020

Status

approved