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A320771 Primes p for which p-1 and p+1 are Niven numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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 A084736

Adjacent sequences:  A320768 A320769 A320770 * A320772 A320773 A320774

KEYWORD

nonn,base

AUTHOR

Marius A. Burtea, Oct 21 2018

STATUS

approved

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)