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User:Charles R Greathouse IV/Favorites

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Of course no collection of "favorite" sequences can be canonical, or exhaustive, but these sequences are some that struck me as especially nice and which I wanted to record for future reference. You may enjoy them too!

By author

This is a collection of some of my favorite sequences from these authors. Tastes vary, but I think these are nice.

  • A Joerg Arndt: A065428, Numbers n such that no are prime.
  • B Roger Lee Bagula: A167660, Chocolate dove bar numerator:
  • John Michael Bergot: A154598, a(n) = smallest prime p such that p-1 and p+1 both have n prime factors.
  • C Pierre CAMI: A115563, Decimal expansion of
  • Eric Chen: A253236, The unique prime p <= n such that n-th cyclotomic polynomial has a root mod p, or 0 if no such p exists.
  • Marius Coman A214305, Fermat pseudoprimes to base 2 with two prime factors.
  • Paul Curtz: A172412, Multiples of 4 with the property that addition of a square gives a square that is not larger than the square for any later term.
  • D Mark Dols: A151982, Arrangement of Fibonacci-numbers in a centered triangular fashion, such that every number is the difference and/or sum of adjacent numbers.
  • E Jason Earls: A050150, Odd numbers with prime number of divisors.
  • Rémi Eismann: A117078, a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.
  • Labos Elemer: A082885, Primes followed by a larger-than-average prime gap.
  • F Odimar Fabeny: A101402, a(0)=0, a(1)=1; for n>=2, let k = smallest power of 2 that is >= n, then a(n) = a(k/2) + a(n-1-k/2).
  • G Gerasimov Sergey: pseudonym of Juri-Stepan Gerasimov
  • Sergey Gerasimov: pseudonym of Juri-Stepan Gerasimov
  • Irina Gerasimova: pseudonym of Juri-Stepan Gerasimov
  • Juri-Stepan Gerasimov: A166955, is a perfect power.
  • Charles R Greathouse IV: A173419, Length of shortest computation yielding n using addition, subtraction and multiplication.
  • Ilya Gutkovskiy: A263653, a(n) =
  • H Enoch Haga: A046731, Sum of primes < 10^n.
  • Michael Joseph Halm: A081357, Sublime numbers, numbers for which the number of divisors and the sum of the divisors are both perfect.
  • Syed Iddi Hasan: A215966, Number of ways prime(n) can be expressed as the sum of distinct smaller noncomposites.
  • J. W. Helkenberg: A181732, Numbers n such that 90n + 1 is prime.
  • K Agaram Kandadai Devaraj: A162290, the Pomerance index of the n-th 3-Carmichael number.
  • Clark Kimberling: A025527,
  • L Michel Nicole Lagneau: A206709, Number of primes of the form for
  • Ilya Lopatin: pseudonym of Juri-Stepan Gerasimov
  • Moshe Levin: pseudonym of Zak Seidov
  • Vincenzo Librandi: A172028, a(1) = 2; for n > 1, a(n) = smallest k such that a(n-1)^3+k is a cube.
  • M James G. Merickel: A171810, The least k>0 such that is irreducible.
  • N Naohiro Nomoto: A058377, Number of solutions to
  • Thomas Nordhaus: A079296, Primes listed in order of their Andrica ranking.
  • O Vladimir Joseph Stephan Orlovsky: A154293, Integers of the form t/6, where t = A000217(m) is a triangular number.
  • P Omar Evaristo Pol: A161914, Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14.
  • Jonathan Vos Post: A100200, Decimal Gödelization of antitheorems from propositional calculus, in Richard Schroeppel's metatheory of A101273.
  • Ki Punches: A161002, Least prime of three consecutive primes (p1,p2,p3) such that p2-p1 and p3-p2 are both perfect squares.
  • R Viswanathan Raman: A216503, a(n) = number of positive integers k such that has a solution with x>0, y>0.
  • Alena Rittina: pseudonym of Juri-Stepan Gerasimov
  • Felice Russo: A045917, From Goldbach problem: number of decompositions of 2n into unordered sums of two primes.
  • S Zakir F. Seidov: A074981, Conjectured list of positive numbers which are not of the form where r,s,i,j are integers with r>0, s>0, i>1, j>1.
  • Nadezda Sokirka: pseudonym of Juri-Stepan Gerasimov
  • Michael Somos: A186704, the minimum number of distinct distances determined by n points in the Euclidean plane.
  • Carmine Suriano: A178576, Primes that are the sum of two Fibonacci numbers.
  • T Giovanni Teofilatto: A123193, Natural numbers with number of divisors equal to a Fibonacci number.
  • W Arkadiusz Wesolowski: A180247, Prime Brier numbers: prime n such that for all k >= 1 the numbers n*2^k + 1 and n*2^k - 1 are composite.
  • David W. Wilson: A023193, Largest number of pairwise coprime numbers that can occur in an interval of length n.
  • Z Eva-Maria Zschorn: A172271, Smaller member p of a twin prime pair (p,p+2) with a cube sum N^3.

If your name's not here, don't worry; there are thousands of authors on the OEIS and I haven't included choices for them all. Still, I may expand the list as time permits.

If you would like to be included, please leave a note on my Talk page or send me (crgreathouse (at) an email with your best half-dozen sequences. I can't promise I'll get to it quickly, and of course our tastes may not match. Please send at most one (your best!) 'base' sequence.

By keyword

This is a collection of some of my favorite sequences with these keywords. Nonmathematical sequences are traditionally marked "dumb", but that doesn't mean they aren't interesting, for example.

  • base: A005349, Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
  • dumb: A215009, Numbers which are "easy" to key on a computer numpad.