A081981 Primes p such that p+1 is divisible by every nonzero digit of p.

11, 23, 101, 113, 131, 167, 211, 233, 263, 269, 311, 359, 383, 431, 443, 727, 863, 1013, 1021, 1031, 1061, 1103, 1163, 1201, 1217, 1223, 1259, 1301, 1361, 1427, 1439, 1601, 1613, 1619, 1637, 1721, 1777, 1823, 1847, 2003, 2011, 2063, 2069, 2111, 2213, 2221

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = 576n log n + O(n^0.955), since primes = 2519 mod 2520 are all in this sequence, and almost all (in the sense of natural density) terms of this sequence are of that form. - Charles R Greathouse IV, Sep 06 2022

Example

167 is a member as 168 is divisible by 1, 6 and 7.

Prog

(Python)
from sympy import isprime
def ok(n): return all((n+1)%int(d) == 0 for d in set(str(n)) - {"0"}) and isprime(n)
print([k for k in range(2222) if ok(k)]) # Michael S. Branicky, Sep 06 2022

Crossrefs

Cf. A081982, A081983, A081984, A081986, A081987, A179520.

Sequence in context: A050767 A145918 A077707 * A081982 A092558 A294255

Adjacent sequences: A081978 A081979 A081980 * A081982 A081983 A081984

Keyword

base,nonn

Author

Amarnath Murthy, Apr 04 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

Added "nonzero" to definition following a comment by Harvey Dale. - N. J. A. Sloane, Jan 08 2011.

Status

approved