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.

A256775 Primes of the form n^2 + 81.

Original entry on oeis.org

97, 181, 277, 337, 757, 1237, 2017, 3217, 4177, 5557, 5857, 6481, 7477, 11317, 13537, 16981, 19681, 21397, 33937, 37717, 48481, 51157, 52981, 59617, 62581, 65617, 80737, 84181, 87697, 96181, 102481, 106357, 111637, 119797, 144481, 149077, 155317, 160081
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 11 2015

Keywords

Comments

Conjecture: sequence is infinite.

Links

Crossrefs

subsequence of A045349.
Cf. A010051, A000290; subsequence of A028916.
Primes of form n^2+b^4, b fixed: A002496 (b=1), A243451 (b=2), A256776 (b=4), A256777 (b=5), A256834 (b=6), A256835 (b=7), A256836 (b=8), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).

Programs

  • Haskell
    a256775 n = a256775_list !! (n-1)
a256775_list = [x | x <- map (+ 81) a000290_list, a010051' x == 1]
  • Magma
    [p: p in PrimesUpTo(200000)| IsSquare(p-81)]; // Vincenzo Librandi, Apr 20 2015
  • Mathematica
    Select[Range[400]^2 + 81, PrimeQ] (* Michael De Vlieger, Apr 19 2015 *)
  • PARI
    for(n=1,10^3,if(isprime(p=n^2+81),print1(p,", "))) \\ Derek Orr, Apr 24 2015

A127435 Primes p such that (p-1)^2 + 1 is prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 37, 41, 67, 127, 131, 151, 157, 181, 211, 241, 251, 257, 271, 281, 307, 397, 401, 421, 431, 467, 491, 557, 571, 577, 647, 691, 701, 751, 761, 827, 907, 911, 937, 947, 967, 1061, 1097, 1151, 1277, 1291, 1307, 1321, 1367, 1567, 1571, 1861
Offset: 1

Views

Author

Lekraj Beedassy, Jan 14 2007

Keywords

Comments

Consists of 3 and a subsequence of A045349.
These are the primes of the form A067720(k)+1. - Michel Marcus, Nov 21 2020

Links

Crossrefs

For the associated primes, see A127436.
Cf. A045349, A067720.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime((p^2-2*p+2))]; // Vincenzo Librandi, Jul 20 2025
  • Mathematica
    Select[Prime@Range[300], PrimeQ[(# - 1)^2 + 1] &] (* Ray Chandler, Jan 23 2007 *)
  • PARI
    listp(nn) = {forprime(p=2, nn, if (isprime((p-1)^2 + 1), print1(p, ", ")););} \\ Michel Marcus, Jun 08 2016

Formula

a(n) = sqrt(A127436(n)-1) + 1.

Extensions

Corrected and extended by Ray Chandler, Jan 23 2007

A127436 Primes associated with A127435.

Original entry on oeis.org

2, 5, 17, 37, 101, 257, 1297, 1601, 4357, 15877, 16901, 22501, 24337, 32401, 44101, 57601, 62501, 65537, 72901, 78401, 93637, 156817, 160001, 176401, 184901, 217157, 240101, 309137, 324901, 331777, 417317, 476101, 490001, 562501, 577601, 682277
Offset: 1

Views

Author

Lekraj Beedassy, Jan 14 2007

Keywords

Comments

A sequence with P=a(k) distinct numbers contains a subsequence of p=A127435(k) monotonically increasing or decreasing terms, according to a corollary of the Erdos-Szekeres theorem.

Crossrefs

Cf. A127435. Subsequence of A045349.

Programs

  • Mathematica
    Select[(Prime@Range[300] - 1)^2 + 1, PrimeQ] (* Ray Chandler, Jan 23 2007 *)
  • PARI
    listp(nn) = {forprime(p=2, nn, if (isprime(q=(p-1)^2 + 1), print1(q, ", ")););} \\ Michel Marcus, Jun 08 2016

Formula

a(n) = (A127435(n)-1)^2 + 1.

Extensions

Corrected and extended by Ray Chandler, Jan 23 2007
Showing 1-3 of 3 results.

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

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