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.

A163111 Prime numbers with gaps larger than 18 towards both neighboring primes.

Original entry on oeis.org

3967, 11027, 11657, 14107, 16033, 16787, 18013, 18617, 18637, 18839, 19661, 21247, 23719, 24281, 24571, 29101, 30367, 31357, 32749, 33247, 33679, 33997, 35201, 36037, 37747, 38501, 40063, 40387, 42533, 42611, 43691, 43913, 44417, 46957
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 20 2009

Keywords

Links

Crossrefs

Cf. A137875, A137874, A137873, A137872, A137871

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4]&&!PrimeQ[p-6]&&!PrimeQ[p+6]&& !PrimeQ[p-8]&&!PrimeQ[p+8]&&!PrimeQ[p-10]&&!PrimeQ[p+10]&&!PrimeQ[p-12]&&!PrimeQ[p+12]&&!PrimeQ[p-14]&&!PrimeQ[p+14]&&!PrimeQ[p-16]&&!PrimeQ[p+16]&&!PrimeQ[p-18]&&!PrimeQ[p+18], AppendTo[lst,p]],{n,8!}];lst
Select[Partition[Prime[Range[5000]],3,1],Min[Differences[#]]>18&][[All,2]] (* Harvey P. Dale, Jul 08 2021 *)

Formula

{A000040(i) : A001223(i) > 18 and A001223(i-1) > 18}. - R. J. Mathar, Jul 27 2009

Extensions

Definition rephrased by R. J. Mathar, Jul 27 2009

A163112 Prime numbers with gaps larger than 20 towards both neighboring primes.

Original entry on oeis.org

16033, 16787, 18013, 23719, 24281, 29101, 32749, 33247, 33679, 33997, 37747, 38501, 40063, 40387, 42533, 42611, 44417, 46957, 51109, 51383, 53479, 54217, 55291, 55763, 56333, 56569, 58271, 58511, 58831, 59833, 61441, 61781, 62273, 66137, 66271, 69593, 69623
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 20 2009

Keywords

Comments

Subsequence of A163111.

Links

Crossrefs

Cf. A137875, A137874, A137873, A137872, A137871, A163111.

Programs

  • Maple
    p := 2; q := 3; r := 3; for n from 2 to 15000 do if q-p > 20 and r-q > 20 then printf("%d,",q) ; fi; p := q; q := r; r := nextprime(r) ; od: # R. J. Mathar, Jul 27 2009
  • Mathematica
    Select[Partition[Prime[Range[7000]],3,1],Min[Differences[#]]>20&] [[All, 2]] (* Harvey P. Dale, Mar 16 2017 *)

Formula

{A000040(i) : A001223(i) > 20 and A001223(i-1) > 20}. - R. J. Mathar, Jul 27 2009

Extensions

Definition rephrased by R. J. Mathar, Jul 27 2009

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
Showing 1-3 of 3 results.

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