cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Examples

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

Links

Crossrefs

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

Programs

  • Maple
    filter:= proc(n)
  isprime(n) and n+1 mod ilcm(subs(0=NULL,convert(n,base,10))) = 0
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Jul 23 2025
  • 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

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

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.

A081982 Primes p such that p+1 is divisible by the digital product (of nonzero digits) of p.

Original entry on oeis.org

11, 23, 101, 113, 131, 167, 211, 233, 311, 431, 863, 1013, 1021, 1031, 1061, 1103, 1201, 1217, 1223, 1259, 1301, 1601, 1619, 1637, 1721, 1823, 2003, 2011, 2111, 2687, 3011, 3023, 3203, 4111, 4703, 6011, 6047, 6101, 6173, 6263, 6911, 7013
Offset: 1

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Comments

Contains A020449 and A107612 (except 2). - Robert Israel, Nov 09 2017

Examples

			167 is a term as 168 is divisible by 1*6*7 = 42.

Links

Crossrefs

Cf. A020449, A081981, A081983, A081984, A081986, A081987, A107612, A101987.

Programs

  • Maple
    filter:= proc(n)
isprime(n) and
n+1 mod convert(subs(0=NULL,convert(n,base,10)),`*`) = 0
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Nov 09 2017
  • PARI
    isok(p) = isprime(p) && (d=digits(p)) && !((p+1) % prod(k=1, #d, if (d[k], d[k], 1))); \\ Michel Marcus, Nov 09 2017

Extensions

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

A081983 Primes p such that p-1 is divisible by every nonzero digit of p.

Original entry on oeis.org

11, 13, 19, 31, 41, 61, 71, 101, 103, 109, 127, 151, 163, 199, 211, 223, 241, 251, 281, 313, 331, 337, 379, 401, 421, 433, 521, 541, 601, 613, 631, 661, 673, 701, 881, 919, 991, 1009, 1021, 1033, 1051, 1063, 1123, 1151, 1201, 1213, 1231, 1303, 1321, 1481
Offset: 1

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Examples

			127 is a member as 126 is divisible by 1, 2 and 7.

Links

Crossrefs

Cf. A081981, A081982, A081984, A081986, A081987.

Programs

  • Mathematica
    Select[Prime[Range[250]],And@@Divisible[#-1,Select[IntegerDigits[ #], #!=0&]]&] (* Harvey P. Dale, Apr 14 2018 *)

Extensions

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

A081984 Primes p such that p-1 is divisible by the digital product ( of nonzero digits) of p.

Original entry on oeis.org

11, 13, 19, 31, 41, 61, 71, 101, 103, 109, 127, 151, 163, 211, 241, 251, 379, 401, 433, 521, 541, 601, 613, 631, 701, 1009, 1021, 1051, 1063, 1123, 1151, 1201, 1213, 1231, 1321, 1511, 1531, 1621, 1723, 1801, 2011, 2017, 2081, 2111, 2113, 2131, 2161, 2311
Offset: 1

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Examples

			127 is a member as 126 is divisible by 1*2*7 =14.

Crossrefs

Cf. A081981, A081982, A081983, A081986, A081987.

Extensions

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

A081987 a(n) = {A081982(n)+1}/d, where d is the product of nonzero digits of A081982(n).

Original entry on oeis.org

12, 4, 102, 38, 44, 4, 106, 13, 104, 36, 6, 338, 511, 344, 177, 368, 601, 87, 102, 14, 434, 267, 30, 13, 123, 38, 334, 1006, 1056, 4, 1004, 168, 178, 1028, 56, 1002, 36, 1017, 49, 29, 128, 334, 6, 1014, 46, 478, 1677, 160, 3368, 10112, 1126, 5106, 852, 183, 114
Offset: 1

Views

Author

Amarnath Murthy, Apr 04 2003

Keywords

Examples

			A081982(6) = 167 hence a(6) = 168/(1*6*7) = 4.

Crossrefs

Cf. A081981, A081982, A081983, A081984, A081986.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.