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
Examples
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.
Links
- Marius A. Burtea, Table of n, a(n) for n = 1..11188
Programs
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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
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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
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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 *)
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PARI
isniven(n) = frac(n/sumdigits(n)) == 0; isok(p) = isprime(p) && isniven(p-1) && isniven(p+1); \\ Michel Marcus, Oct 22 2018
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