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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 (list; graph; refs; listen; history; text; internal format)
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.

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.

Sequence in context: A002810 A045736 A158807 * A067006 A136020 A076304

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

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Last modified April 17 16:59 EDT 2021. Contains 343063 sequences. (Running on oeis4.)