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 1-3 of 3 results.

A167833 Three-times-isolated primes: primes p such that neither p+-2, p+-4 nor p+-6 is prime.

Original entry on oeis.org

2, 211, 293, 409, 479, 631, 691, 701, 709, 719, 787, 797, 839, 919, 929, 1163, 1171, 1201, 1249, 1259, 1381, 1399, 1409, 1471, 1511, 1523, 1531, 1637, 1709, 1733, 1801, 1811, 1823, 1831, 1847, 1889, 2039, 2053, 2099, 2153, 2161, 2179, 2221, 2251, 2459
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2009

Keywords

Comments

2 together with prime numbers, isolated from neighboring primes by>6.

Examples

			a(1)=2 (-4,-2,0,4,6,8 are nonprimes); a(2)=211 (205,207,209,213,215,217 are nonprimes).

Links

Crossrefs

Cf. A137870, A167771.

Programs

  • Mathematica
    Join[{2},Select[Prime[Range[400]],NoneTrue[#+{2,4,6,-2,-4,-6},PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 16 2019 *)

A167838 Four-times-isolated primes: primes p such that neither p+-2, p+-4, p+-6 nor p+-8 is prime.

Original entry on oeis.org

2, 211, 293, 631, 787, 797, 839, 1249, 1259, 1399, 1409, 1471, 1511, 1637, 1709, 1801, 1811, 1847, 1889, 2039, 2053, 2099, 2179, 2503, 2521, 2579, 2633, 2647, 2767, 2777, 2819, 2927, 2939, 3109, 3137, 3271, 3433, 3571, 3593, 3659, 3779, 3833, 3863, 3967
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2009

Keywords

Comments

2 together with (A137871: prime numbers isolated from neighboring primes by more than 8).

Examples

			a(1)=2 (-6,-4,-2,0,4,6,8,10 are nonprimes); a(2)=211 (203,205,207,209,213,215,217,219 are nonprimes).

Links

Crossrefs

Cf. A137871, A167771.

Programs

  • Maple
    Primes:= select(isprime, {2,seq(i,i=3..10000,2)}):
S:=Primes minus `union`(seq(map(`+`,Primes, i),i=[-2,2,-4,4,-6,6,-8,8])):
sort(convert(S,list)); # Robert Israel, Jun 19 2016

Extensions

Corrected by Robert Israel, Jun 19 2016

A167840 Six-times-isolated primes: primes p such that none of p+-2, p+-4, p+-6, p+-8, p+-10 nor p+-12 are prime.

Original entry on oeis.org

2, 1847, 2179, 2503, 2819, 3137, 3433, 3967, 4177, 4621, 4831, 5623, 5953, 6637, 7283, 7369, 7393, 7433, 7621, 7993, 8039, 8147, 9257, 9587, 10753, 11027, 11197, 11213, 11369, 11657, 13063, 13367, 13381, 13537, 13553, 13649, 13859, 14107, 14221, 14369, 14503
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2009, Mar 26 2010

Keywords

Comments

Essentially the same as A137873. - R. J. Mathar, Dec 06 2009

Examples

			a(1)=2 (-10,-8,-6,-4,-2,0,4,6,8,10,12 are nonprimes);
a(2)=1847 (1835,1837,1839,1841,1843,1845,1849,1851,1853,1855,1857,1859 are nonprimes).

Links

Crossrefs

Cf. A000040, A137873, A167771, A167839.

Programs

  • Maple
    q:= p-> not ormap(isprime, [seq([p+i, p-i][], i=2..12, 2)]):
select(q, [ithprime(i)$i=1..2000])[];  # Alois P. Heinz, Jan 03 2022

Extensions

More terms from Dmitry Kamenetsky, Nov 30 2009
Missing term 13553 inserted by Alois P. Heinz, Jan 03 2022
Showing 1-3 of 3 results.

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