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 1-6 of 6 results.

A164926 Least prime p such that x^2+x+p produces primes for x=0..n-1 and composite for x=n.

Original entry on oeis.org

2, 3, 107, 5, 347, 1607, 1277, 21557, 51867197, 11, 180078317, 1761702947, 8776320587, 27649987598537, 291598227841757, 17
Offset: 1

Views

Author

T. D. Noe, Sep 01 2009

Keywords

Comments

Other known values: a(16)=17 and a(40)=41 (which is generated by Euler's polynomial, A005846). There are no other terms less than 10^12. All of Euler's Lucky numbers, A014556, are in this sequence. Assuming the prime k-tuples conjecture, Mollin's theorem 2.1 shows this sequence is defined for n>0.
a(21)=234505015943235329417 found by J. Waldvogel and Peter Leikauf. [Jens Kruse Andersen, Sep 09 2009]

Links

Crossrefs

Cf. A005846, A014556, A067774, A210360, A210361, A210362, A210363, A210364, A210365, A211236, A211237, A211238, A211239, A211240, A354585.

Programs

  • Mathematica
    PrimeRun[p_Integer] := Module[{k=0}, While[PrimeQ[k^2+k+p], k++ ]; k]; nn=8; t=Table[0,{nn}]; cnt=0; p=1; While[cnt

Extensions

a(14) and a(15) from Jens Kruse Andersen, Sep 09 2009

A210360 Prime numbers p such that x^2 + x + p produces primes for x = 0..1 but not x = 2.

Original entry on oeis.org

3, 29, 59, 71, 137, 149, 179, 197, 239, 269, 281, 419, 431, 521, 569, 599, 617, 659, 809, 827, 1019, 1031, 1049, 1061, 1151, 1229, 1289, 1319, 1451, 1619, 1667, 1697, 1721, 1787, 1877, 1931, 1949, 2027, 2087, 2111, 2129, 2141, 2309, 2339, 2381, 2549, 2591
Offset: 1

Views

Author

T. D. Noe, Apr 05 2012

Keywords

Comments

The first term is A164926(2).

Links

Crossrefs

Cf. A067774, A164926, A210361, A210362, A210363, A210364, A210365.

Programs

  • Mathematica
    lookfor = 2; t = {}; n = 0; While[Length[t] < 50, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t

A210362 Prime numbers p such that x^2 + x + p produces primes for x = 0..3 but not x = 4.

Original entry on oeis.org

5, 101, 227, 1091, 1481, 1487, 3917, 4127, 4787, 8231, 9461, 10331, 11777, 12107, 14627, 16061, 20747, 25577, 27737, 29021, 32297, 33347, 35531, 35591, 36467, 38447, 39227, 41177, 42461, 44267, 44531, 49031, 59441, 69191, 77237, 79811, 80777, 93251, 93491
Offset: 1

Views

Author

T. D. Noe, Apr 05 2012

Keywords

Comments

The first term is A164926(4).

Links

Crossrefs

Cf. A067774, A164926, A210360, A210361, A210363, A210364, A210365.

Programs

  • Mathematica
    lookfor = 4; t = {}; n = 0; While[Length[t] < 50, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t
Select[Prime[Range[10000]],AllTrue[#+{2,6,12},PrimeQ]&&!PrimeQ[#+20]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 26 2015 *)
Select[Prime[Range[10000]],Boole[PrimeQ[#+{2,6,12,20}]]=={1,1,1,0}&] (* Harvey P. Dale, Nov 17 2024 *)

A210363 Prime numbers p such that x^2 + x + p produces primes for x = 0..4 but not x = 5.

Original entry on oeis.org

347, 641, 1427, 2687, 4001, 4637, 4931, 19421, 21011, 22271, 23741, 26711, 27941, 32057, 43781, 45821, 55331, 55817, 68207, 71327, 91571, 128657, 165701, 167621, 172421, 179897, 191447, 193871, 205421, 234191, 239231, 258107, 258611, 259157, 278807, 290021
Offset: 1

Views

Author

T. D. Noe, Apr 05 2012

Keywords

Comments

The first term is A164926(5).

Links

Crossrefs

Cf. A067774, A164926, A210360, A210361, A210362, A210364, A210365.

Programs

  • Mathematica
    lookfor = 5; t = {}; n = 0; While[Length[t] < 50, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t
Select[Prime[Range[26000]],AllTrue[#+{2,6,12,20},PrimeQ] && !PrimeQ[ #+30]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2017 *)
Select[Prime[Range[26000]],Boole[PrimeQ[#+{2,6,12,20,30}]]=={1,1,1,1,0}&] (* Harvey P. Dale, May 29 2025 *)

A210364 Prime numbers p such that x^2 + x + p produces primes for x = 0..5 but not x = 6.

Original entry on oeis.org

1607, 3527, 13901, 31247, 33617, 55661, 68897, 97367, 166841, 195731, 221717, 347981, 348431, 354371, 416387, 506327, 548831, 566537, 929057, 954257, 1246367, 1265081, 1358801, 1505087, 1538081, 1595051, 1634441, 1749257, 2200811, 2322107, 2641547, 2697971
Offset: 1

Views

Author

T. D. Noe, Apr 05 2012

Keywords

Comments

The first term is A164926(6).

Links

Crossrefs

Cf. A067774, A164926, A210360, A210361, A210362, A210363, A210365.

Programs

  • Mathematica
    lookfor = 6; t = {}; n = 0; While[Length[t] < 50, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t

A210365 Prime numbers p such that x^2 + x + p produces primes for x = 0..6 but not x = 7.

Original entry on oeis.org

1277, 28277, 113147, 421697, 665111, 1164587, 1615631, 2798921, 2846771, 3053747, 5071667, 5093507, 5344247, 5706641, 6383051, 8396777, 10732817, 10812407, 11920367, 13176587, 16197947, 16462541, 16655447, 16943471, 17807831, 18102101, 20488901, 23421311
Offset: 1

Views

Author

T. D. Noe, Apr 05 2012

Keywords

Comments

The first term is A164926(7).

Links

Crossrefs

Cf. A067774, A164926, A210360, A210361, A210362, A210363, A210364.

Programs

  • Mathematica
    lookfor = 7; t = {}; n = 0; While[Length[t] < 30, n++; c = Prime[n]; i = 1; While[PrimeQ[i^2 + i + c], i++]; If[i == lookfor, AppendTo[t, c]]]; t
Showing 1-6 of 6 results.

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