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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)).
2
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
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
KEYWORD
nonn
AUTHOR
Ahmad J. Masad, Nov 15 2020
EXTENSIONS
More terms from Michel Marcus, Nov 17 2020
STATUS
approved