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 1-5 of 5 results.

A129484 Primes of the form 17k + 1.

Original entry on oeis.org

103, 137, 239, 307, 409, 443, 613, 647, 919, 953, 1021, 1123, 1259, 1327, 1361, 1429, 1531, 1667, 1871, 1973, 2143, 2347, 2381, 2551, 2687, 2789, 2857, 3061, 3163, 3299, 3469, 3571, 3673, 3877, 3911, 4013, 4217, 4421, 4523, 4591, 4931, 4999, 5101, 5237
Offset: 1

Views

Author

Cino Hilliard, May 29 2007

Keywords

Links

Crossrefs

Cf. A140544, A092074, A094657, A138623, A140545, A138629, A138633, A138631, A138627, A140542, A138625, A141865, A140540, A140543, A140541.

Programs

  • Magma
    [n: n in [1..5000 by 17] | IsPrime(n)] ; // Vincenzo Librandi, Apr 04 2011
  • Mathematica
    Select[Range[1,5000,17],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011 *)
  • PARI
    cicadayear(n) = forstep(x=1,n,17,if(isprime(x),print1(x",")))

A138631 Primes of the form 17*k + 9.

Original entry on oeis.org

43, 179, 281, 349, 383, 587, 757, 859, 1063, 1097, 1301, 1471, 1607, 1709, 1777, 1811, 1879, 1913, 2083, 2287, 2389, 2423, 2593, 2729, 2797, 3001, 3137, 3307, 3511, 3613, 3851, 3919, 4021, 4157, 4259, 4327, 4463, 4871, 4973, 5279, 5347, 5381, 5449, 5483
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 14 2008

Keywords

Examples

			17*2 + 9 = 43, 17*10 + 9 = 179, 17*16 + 9 = 281, 17*20 + 9 = 349, 17*22 + 9 = 349, ...

Links

Crossrefs

Cf. A138632.
Primes congruent to k mod 17: A129484 (k=1), A140544 (k=2), A092074 (k=3), A094657 (k=4), A138623 (k=5), A140545 (k=6), A138629 (k=7), A138633 (k=8), this sequence (k=9), A138627 (k=10), A140542 (k=11), A138625 (k=12), A141865 (k=13), A140540 (k=14), A140543 (k=15), A140541 (k=16).

Programs

  • Mathematica
    a={};Do[x=17*n+9;If[PrimeQ[x],AppendTo[a,x]],{n,10^2}];a
Select[17*Range[350]+9,PrimeQ] (* Harvey P. Dale, May 14 2017 *)

Formula

From A.H.M. Smeets, Sep 05 2019: (Start)
a(n)/log(a(n)) ~ 16*n;
Integral_{x=2..a(n)} dx/log(x) ~ 16*n. (End)

Extensions

More terms from N. J. A. Sloane, Jul 11 2008

A138633 Primes of the form 17*k - 9.

Original entry on oeis.org

59, 127, 229, 263, 331, 433, 467, 569, 739, 773, 977, 1181, 1249, 1283, 1453, 1487, 1657, 1759, 1861, 1997, 2099, 2269, 2371, 2473, 2609, 2677, 2711, 3119, 3187, 3221, 3323, 3391, 3527, 3697, 3833, 4003, 4139, 4241, 4513, 4547, 4649, 4751, 5023, 5227, 5261
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 14 2008

Keywords

Examples

			17*4 - 9 = 59, 17*8 - 9 = 127, 17*14 - 9 = 229, 17*16 - 9 = 263, 17*20 - 9 = 331, 17*26 - 9 = 433, 17*28 - 9 = 467, ...

Links

Crossrefs

Cf. A138634.
Primes congruent to k mod 17: A129484 (k=1), A140544 (k=2), A092074 (k=3), A094657 (k=4), A138623 (k=5), A140545 (k=6), A138629 (k=7), this sequence (k=8), A138631 (k=9), A138627 (k=10), A140542 (k=11), A138625 (k=12), A141865 (k=13), A140540 (k=14), A140543 (k=15), A140541 (k=16).

Programs

  • Mathematica
    a={};Do[x=17*n-9;If[PrimeQ[x],AppendTo[a,x]],{n,10^2}];a
Select[17*Range[400]-9,PrimeQ] (* Harvey P. Dale, Jul 25 2020 *)

Formula

From A.H.M. Smeets, Sep 05 2019: (Start)
n ~ (1/16) * a(n)/log(a(n)).
n ~ (1/16) * Integral_{x=2..a(n)} dx/log(x). (End)

Extensions

More terms from N. J. A. Sloane, Jul 11 2008

A154612 a(n) = 17*n + 7.

Original entry on oeis.org

7, 24, 41, 58, 75, 92, 109, 126, 143, 160, 177, 194, 211, 228, 245, 262, 279, 296, 313, 330, 347, 364, 381, 398, 415, 432, 449, 466, 483, 500, 517, 534, 551, 568, 585, 602, 619, 636, 653, 670, 687, 704, 721, 738, 755, 772, 789, 806, 823, 840, 857, 874, 891
Offset: 0

Views

Author

Vincenzo Librandi, Jan 15 2009

Keywords

Comments

a(n)^4 = Sum_{j=0..(16*n*(17*n+14)+46)} (-1)^j*(119*n^2 + 98*n + 20 + j)^2. - Bruno Berselli, Apr 30 2010

Examples

			For n=5, a(5)^4 = 92^4 = 71639296 = 3485^2-3486^2+3487^2-..+11449^2-11450^2+11451^2. - _Bruno Berselli_, Apr 30 2010

Links

Crossrefs

Cf. A138629, A138630.
Sequences of the form 17*n+q: A361692 (q=-1), A008599 (q=0), A215137 (q=1), this sequence (q=7).

Programs

Formula

G.f.: (7+10*x)/(1-x)^2. - Colin Barker, Jan 09 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 26 2012
E.g.f.: (7 + 17*x)*exp(x). - G. C. Greubel, May 31 2024

Extensions

Offset corrected by Bruno Berselli, Aug 16 2010

A274202 Primes congruent to 31 mod 65.

Original entry on oeis.org

31, 421, 811, 941, 1201, 1721, 2111, 2371, 3541, 3671, 3931, 4451, 5101, 5231, 5881, 6011, 6271, 6661, 6791, 8221, 8741, 9001, 9391, 9521, 9781, 10301, 10691, 11471, 11731, 12251, 12511, 12641, 13291, 13421, 13681, 14071, 14461, 14591, 14851, 15241, 15761
Offset: 1

Views

Author

Vincenzo Librandi, Jun 13 2016

Keywords

Comments

Subsequence of A030430 and A102732.

Links

Crossrefs

Cf. A000040, A030430, A102732.
Cf. similar sequences of the type primes congruent to k mod 2*k+3: A045392 (k=2), A102732 (k=5), A138629 (k=7), A141873 (k=8), A141914 (k=10), A141935 (k=11), A141989 (k=13), A142018 (k=14), A142086 (k=16), A142126 (k=17), A142216 (k=19), A142269 (k=20), A142373 (k=22), A142433 (k=23), A142555 (k=25), A142619 (k=26), A142755 (k=28), A142827 (k=29), this sequence (k=31), A154621 (k=32), A154624 (k=34), A154628 (k=35).

Programs

  • Magma
    [p: p in PrimesUpTo(20000) | p mod 65 eq 31];
  • Mathematica
    Select[Prime[Range[2000]], MemberQ[{31}, Mod[#, 65]] &]
Select[Range[31,16000,65],PrimeQ] (* Harvey P. Dale, May 06 2018 *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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