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.

A248549 Numbers n such that the smallest prime divisor of n^2+1 is 61.

Original entry on oeis.org

194, 316, 416, 804, 904, 926, 1026, 1170, 1270, 1414, 1536, 1780, 2024, 2490, 2734, 2856, 3000, 3100, 3244, 3344, 3366, 3610, 3954, 3976, 4320, 4564, 4830, 4930, 5074, 5196, 5540, 5684, 6394, 6416, 6516, 6760, 6904, 7004, 7126, 7270, 7370, 7514, 7614, 7736
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(9).
a(n)== 50 or 72 (mod 122).

Examples

			194 is in the sequence because 194^2+1= 61*617.

Links

Crossrefs

Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.

Programs

  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==61, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 61; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[8000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

A248553 Numbers n such that the smallest prime divisor of n^2+1 is 101.

Original entry on oeis.org

10, 414, 596, 1000, 1020, 1606, 1626, 2030, 2414, 2434, 2616, 3444, 3626, 3646, 4030, 5040, 5060, 5646, 5666, 6070, 6454, 6474, 6656, 6676, 7060, 7464, 7666, 7686, 8070, 8090, 8474, 8696, 9080, 9504, 10090, 10494, 10696, 10716, 11504, 11706, 12534, 12716, 12736
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(13).
a(n)== 10 or 192 (mod 202).

Examples

			414 is in the sequence because 414^2+1= 101*1697.

Links

Crossrefs

Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.

Programs

  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==101, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 101; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[13000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
Select[Range[13000],FactorInteger[#^2+1][[1,1]]==101&] (* Harvey P. Dale, Oct 01 2024 *)

A248532 Numbers n such that the smallest prime divisor of n^2+1 is 53.

Original entry on oeis.org

76, 136, 454, 500, 560, 666, 924, 984, 1196, 1454, 1514, 1666, 1726, 2090, 2196, 2256, 2620, 2726, 2786, 3044, 3104, 3150, 3210, 3256, 3316, 3680, 3786, 4104, 4210, 4270, 4316, 4634, 4694, 4800, 4846, 5224, 5330, 5694, 5800, 5860, 5906, 5966, 6224, 6330, 6390
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(8).
a(n)== 30 or 76 (mod 106).

Examples

			76 is in the sequence because 76^2+1= 53*109.

Links

Crossrefs

Cf. A089120, A002313, A209874, A248527, A248528, A248529, A248530, A248531.

Programs

  • Magma
    [n: n in [2..7000] | PrimeDivisors(n^2+1)[1] eq 53]; // Bruno Berselli, Oct 08 2014
  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==53, AppendTo[lst, n]], {n, 2, 2000}]; lst
Select[Range[7000],FactorInteger[#^2+1][[1,1]]==53&] (* Harvey P. Dale, Aug 04 2016 *)
p = 53; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[7000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

A248550 Numbers n such that the smallest prime divisor of n^2+1 is 73.

Original entry on oeis.org

100, 246, 484, 630, 776, 830, 976, 1506, 1706, 1944, 2144, 2236, 2290, 2874, 3020, 3604, 3696, 3750, 3896, 4134, 4426, 4626, 4864, 5064, 5210, 5356, 5594, 5740, 5794, 5940, 6086, 6324, 6470, 6616, 6670, 6816, 7200, 7254, 7346, 7400, 7546, 7930, 7984, 8076
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(10).
a(n) == 46 or 100 (mod 146).
No need to completely factorize n^2+1. - David A. Corneth, Apr 29 2017

Examples

			100 is in the sequence because 100^2+1= 73*137.
246 is in the sequence because 246^2+1 isn't divisible by any prime less than 73 and is divisible by 73. - _David A. Corneth_, Apr 29 2017

Links

Crossrefs

Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.

Programs

  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==73, AppendTo[lst, n]], {n, 2, 10000}]; lst
Select[Range[8100],FactorInteger[#^2+1][[1,1]]==73&] (* Harvey P. Dale, Apr 29 2017 *)
p = 73; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[8000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
  • PARI
    is(n) = {my(m=n%146, p=2, n21 = n^2+1, v=[5, 13, 17, 29, 37, 41, 53, 61]);
return(abs(73-m)==27&&sum(i=1, #v, p=nextprime(p+1); valuation(n21,v[i]))==0)}
upto(n) = {my(l=List(), i=54, m=46); while(mDavid A. Corneth, Apr 29 2017

A248551 Numbers n such that the smallest prime divisor of n^2+1 is 89.

Original entry on oeis.org

144, 390, 856, 1746, 1814, 1924, 2170, 2526, 2636, 2704, 2814, 3170, 3416, 3594, 3704, 3950, 4060, 4306, 4840, 4950, 5306, 5484, 6374, 6620, 6730, 7086, 7154, 7264, 7866, 7976, 8044, 8154, 8400, 8756, 8866, 9044, 9400, 9646, 9824, 10180, 10290, 11070, 11426
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(11).
a(n)== 34 or 144 (mod 178).

Examples

			144 is in the sequence because 144^2+1= 89*233.

Links

Crossrefs

Cf. A089120,A002313,A209874,A248527-A248531,A248549-A248553.

Programs

  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==89, AppendTo[lst, n]], {n, 2, 10000}]; lst
p = 89; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[12000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)

A248552 Numbers n such that the smallest prime divisor of n^2+1 is 97.

Original entry on oeis.org

366, 410, 604, 754, 1336, 1530, 1574, 2156, 2500, 2544, 2694, 3126, 3276, 3470, 3514, 3664, 4096, 4290, 4440, 5066, 5454, 5604, 6186, 6230, 6380, 6424, 6574, 7156, 8126, 8170, 8320, 9140, 9334, 9484, 9916, 10066, 10110, 10260, 10454, 11036, 11230, 11424, 11856
Offset: 1

Views

Author

Michel Lagneau, Oct 08 2014

Keywords

Comments

Or numbers n such that the smallest prime divisor of n^2+1 is A002313(12).
a(n)== 22 or 172 (mod 194).

Examples

			366 is in the sequence because 366^2+1= 97*1381.

Links

Crossrefs

Cf. A089120, A002313, A209874, A248527-A248531, A248549-A248553.

Programs

  • Mathematica
    lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==97, AppendTo[lst, n]], {n, 2, 10000}]; lst
Select[Range[12000],FactorInteger[#^2+1][[1,1]]==97&] (* Harvey P. Dale, Aug 11 2017 *)
p = 97; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[12000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
Showing 1-6 of 6 results.

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