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 1-8 of 8 results.

A216496 Primes that are not in A094383.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 47, 61, 67, 71, 73, 89, 109, 137, 179, 211, 277, 337, 379, 499, 557
Offset: 1

Views

Author

Alex Ratushnyak, Sep 08 2012

Keywords

Comments

Conjecture: a(25)=557 is the last term.

Crossrefs

Cf. A216495, A094383, A216497, A216498, A216468.

Programs

  • Mathematica
    prms = 3; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[PrimePi[10000]]], ! fQ[#] &] (* T. D. Noe, Sep 08 2012 *)

A216495 Primes p with property that there exists a number d>0 such that numbers p-d, p-2*d are primes.

Original entry on oeis.org

7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283
Offset: 1

Views

Author

Alex Ratushnyak, Sep 08 2012

Keywords

Comments

Conjecture: only 5 primes are not in the sequence: 2, 3, 5, 13, 37.

Links

Crossrefs

Cf. A094383, A216497, A216498, A216468.

Programs

  • Mathematica
    prms = 2; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[283]]], fQ] (* T. D. Noe, Sep 08 2012 *)
  • PARI
    is(n)=my(t); forprime(p=2,n-4,if(isprime((t=(n-p)\2)+p) && isprime(2*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

A216468 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...6, are six primes.

Original entry on oeis.org

907, 1307, 1439, 1459, 1669, 1879, 2089, 2141, 2351, 2713, 4139, 4759, 4969, 5179, 5417, 6047, 6101, 6353, 6779, 6793, 7919, 8369, 8663, 9049, 9349, 9491, 9533, 9623, 9769, 10099, 10691, 10883, 11083, 11213, 11369, 11399, 11621, 11789, 11887, 11923, 12097, 12119
Offset: 1

Views

Author

Alex Ratushnyak, Sep 07 2012

Keywords

Comments

Conjecture: only 312722 primes are not in the sequence: 2, 3, ..., 198702899.

Examples

			907 is in the sequence because with d = 150: 7, 157, 307, 457, 607, 757 are all primes.

Crossrefs

Cf. A215895, A216495, A094383, A216497, A216498.

Programs

  • Mathematica
    fQ[p_] := Module[{d = 1}, While[6*d < p && Union[PrimeQ[p - Range[6]*d]] != {True}, d++]; 6*d < p]; Select[Prime[Range[4, PrimePi[12119]]], fQ] (* T. D. Noe, Sep 07 2012 *)
  • PARI
    is(n)=my(t); forprime(p=2,n-20,if((n-p)%6==0 && isprime((t=(n-p)/6)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

A216497 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...4, are four primes.

Original entry on oeis.org

29, 53, 127, 131, 157, 173, 197, 227, 251, 257, 271, 283, 293, 311, 353, 373, 389, 397, 421, 443, 449, 463, 479, 509, 521, 587, 607, 613, 617, 661, 673, 677, 691, 719, 757, 761, 811, 821, 823, 839, 853, 859, 863, 881, 887, 907, 911, 941, 953, 967, 983, 997, 1013
Offset: 1

Views

Author

Alex Ratushnyak, Sep 08 2012

Keywords

Comments

Conjecture: only 653 primes are not in the sequence: 2, 3, ..., 100291.

Examples

			29 is in the sequence because with d=6: 23, 17, 11, 5 are all primes.

Crossrefs

Cf. A216495, A094383, A216498, A216468.

Programs

  • Mathematica
    prms = 4; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[1013]]], fQ] (* T. D. Noe, Sep 08 2012 *)
  • PARI
    is(n)=my(t); forprime(p=2,n-12,if((n-p)%4==0 && isprime((t=(n-p)/4)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

A216498 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...5, are five primes.

Original entry on oeis.org

157, 257, 311, 353, 463, 509, 691, 757, 823, 839, 881, 907, 941, 953, 1063, 1097, 1223, 1229, 1249, 1297, 1301, 1307, 1439, 1459, 1531, 1583, 1669, 1723, 1777, 1879, 1907, 1913, 1931, 2027, 2087, 2089, 2141, 2143, 2179, 2207, 2293, 2351, 2371, 2377, 2399, 2411
Offset: 1

Views

Author

Alex Ratushnyak, Sep 08 2012

Keywords

Comments

Conjecture: only 9198 primes are not in the sequence: 2, 3, ..., 2521081.

Examples

			157 is in the sequence because with d=30: 127, 97, 67, 37, 7 are all primes.

Crossrefs

Cf. A216495, A094383, A216497, A216468.

Programs

  • Mathematica
    prms = 5; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[2411]]], fQ] (* T. D. Noe, Sep 08 2012 *)
  • PARI
    is(n)=my(t); forprime(p=2,n-16,if((n-p)%5==0 && isprime((t=(n-p)/5)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

A094382 Number of quadruples (p, p+d, p+2*d, p+3*d) of primes with d>0 and p+3*d<=n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 28 2004

Keywords

Examples

			a(50)=4: 5=prime(3) -> 5+6=11=prime(5) -> 11+6=17=prime(7) ->
17+6=23=prime(9), 5=prime(3) -> 5+12=17=prime(7) -> 17+12=29=prime(10) ->
29+12=41=prime(13), 7=prime(4) -> 7+12=19=prime(8) -> 19+12=31=prime(11) ->
31+12=43=prime(14) and 11=prime(5) -> 11+6=17=prime(7) -> 17+6=23=prime(9)
-> 23+6=29=prime(10),

Links

Crossrefs

Cf. A093354, A094383.

A216590 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...7, are seven primes.

Original entry on oeis.org

1669, 1879, 2089, 2351, 4969, 5179, 6047, 10883, 11923, 12097, 12143, 12329, 12539, 12763, 13049, 13183, 15413, 15923, 16187, 16547, 16741, 17189, 17581, 18481, 19993, 20201, 21433, 21727, 22303, 22483, 23021, 23053, 23831, 24023, 24749, 25579, 25633, 26111, 26561
Offset: 1

Views

Author

Alex Ratushnyak, Sep 09 2012

Keywords

Comments

Conjecture: only 5254157 primes are not in the sequence: 2, 3, ..., 5082095279.
Conjecture: for any k>0 there exists p0 such that for any prime p>p0 there exists a k-term arithmetic progression of primes with p at the end.

Examples

			1669 is in the sequence because with d=210: 1459, 1249, 1039, 829, 619, 409, 199 are all primes.

Crossrefs

Cf. A216495, A094383, A216497, A216498, A216468.

Programs

  • PARI
    is(n)=my(t); forprime(p=2,n-26,if((n-p)%7==0 && isprime((t=(n-p)/7)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(6*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

A216539 Largest prime p such that there is no n-term arithmetic progression of primes ending with p.

Original entry on oeis.org

2, 37, 557, 100291, 2521081, 198702899, 5082095279
Offset: 2

Views

Author

Alex Ratushnyak, Sep 12 2012

Keywords

Comments

For n>=3, the value given is only a conjecture.

Examples

			It is conjectured (A216495) that 37 is the largest prime p with no 3-term arithmetic progression ending with p. This would imply a(3)=37. (7,19,31, for example, is a progression ending with 31.)

Crossrefs

A216495 conjectures a(3).
A094383 conjectures a(4).
A216497 conjectures a(5).
A216498 conjectures a(6).
A216468 conjectures a(7).
A216590 conjectures a(8).
Cf. A005115.
Showing 1-8 of 8 results.

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