A320771 Primes p for which p-1 and p+1 are Niven numbers.

2, 3, 5, 7, 11, 19, 41, 71, 101, 109, 113, 151, 191, 199, 223, 229, 307, 401, 409, 449, 593, 701, 881, 911, 1009, 1013, 1091, 1129, 1231, 1301, 1303, 1451, 1559, 1811, 1999, 2029, 2089, 2213, 2281, 2311, 2351, 2399, 2531, 2609, 2711, 2753, 3037, 3079, 3109, 3221, 3251, 3329

Offset

1,1

Comments

All of the prime numbers in sequences A253213, A199684, A199687 are part of the sequence.

Links

Marius A. Burtea, Table of n, a(n) for n = 1..11188

Example

For p = 11, p-1 = 10 and p + 1 = 12. 10 is divisible by 1 = 1 + 0, 12 is divisible by 3 = 1 + 2. Thus, p = 11 is a term.
For p = 229, p-1 = 228 and p + 1 = 230. 228 is divisible by 12 = 2 + 2 + 8, and 230 is divisible by 5 = 2 + 3 + 0. Thus, p = 229 is a term.

Mathematica

nivenQ[n_] := Divisible[n, Total[IntegerDigits[n]]]; Select[Range[10000], PrimeQ[#] && nivenQ[#-1] && nivenQ[#+1] &] (* Amiram Eldar, Oct 31 2018 *)
nnQ[p_]:=Divisible[p, Total[IntegerDigits[p]]]; Select[Prime[Range[500]], AllTrue[#+{1, -1}, nnQ]&] (* Harvey P. Dale, Jul 19 2023 *)

Prog

(PARI) isniven(n) = frac(n/sumdigits(n)) == 0;
isok(p) = isprime(p) && isniven(p-1) && isniven(p+1); \\ Michel Marcus, Oct 22 2018
(GAP) Filtered([2..2400], p->IsPrime(p) and (p-1) mod List(List([1..p-1], ListOfDigits), Sum)[p-1]=0 and (p+1) mod List(List([1..p+1], ListOfDigits), Sum)[p+1]=0); # Muniru A Asiru, Oct 29 2018
(Magma) [p: p in PrimesUpTo(2000) | IsIntegral((p-1)/&+Intseq(p-1)) and IsIntegral((p+1)/&+Intseq(p+1))]; // Marius A. Burtea, Jan 06 2019

Crossrefs

Cf. A000040, A005349, A007953, A253213, A177506, A199684, A199687.

Sequence in context: A033274 A071062 A320725 * A002231 A087769 A308510

Adjacent sequences: A320768 A320769 A320770 * A320772 A320773 A320774

Keyword

nonn,base

Author

Marius A. Burtea, Oct 21 2018

Status

approved