David Cushing - cp's OEIS frontend

User: David Cushing

David Cushing has authored 2 sequences.

A238753 Squarefree integers D such that Q(sqrt(D)) contains a non-constant arithmetic progression of 5 squares.

409, 4688329, 250545884330641, 199554894091303668073201, 231574628370557219024862837633967849, 30240048139343876249762998173442832362876517638009, 330823513952828243573122480536077533156064000139119724642295861921

Offset: 1

David Cushing, Mar 04 2014

nonn

Note that there exists no D such that Q(sqrt{D}) contains a non-constant arithmetic progression of 6 squares.

			For D=409, such an arithmetic progression is 49, 169, 289, 409, 529.

Enrique González-Jiménez and Xavier Xarles, Five squares in arithmetic progression over quadratic fields, arXiv:0909.1663 [math.NT], 2009-2013.

A189055 Primes of the form (k+1)^11 - k^11.

Original entry on oeis.org

313968931, 6612607849, 68618940391, 2257404775627, 26360313735014491, 130898631716248441, 11736367906285382977, 28945284114821573731, 229761141540921525811, 202978059247932180748537, 228398127589553102936371, 476213535986962784582617, 1627839264198988265272849, 3421374091098795513254497

Offset: 1

David Cushing, Dec 19 2012

All prime numbers which are the difference of integers raised to the 11th power have this form. Values of n in A211184.

Vladimir Pletser, Table of n, a(n) for n = 1..1000

from itertools import count
primes = Primes()
def diff_pow(i, n):
  return (i+1)**n - i**n
def diff_pow_primes(n, limit=range(1000)):
  pows = [diff_pow(i, n) for i in limit]
  return [p for p in pows if p in primes]
diff_pow_primes(11, count())

cp's OEIS Frontend

User: David Cushing

A238753 Squarefree integers D such that Q(sqrt(D)) contains a non-constant arithmetic progression of 5 squares.

Views

Author

Keywords

Comments

Examples

Links