Andrew R. Booker - cp's OEIS frontend

A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

1, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Altug Alkan, following a suggestion from Andrew R. Booker, Jun 29 2020

Least k such that a(k) = 2^n are 1, 2, 5, 21, 169, 2705, ... (Conjecture: This sequence is A117261).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A130147, A132424, A130535, A283207, A288914, A335898.

f:= proc(n) option remember;
  2*procname(floor((n-1)/procname(n-1))) end proc:
f(1):= 1:
map(f, [$1..105]); # Robert Israel, Jul 08 2020

a[1] = 1; a[n_] := a[n] = 2 * a[Floor[(n-1)/a[n-1]]]; Array[a, 100] (* Amiram Eldar, Jun 29 2020 *)

a=vector(10^3); a[1]=1; for(n=2, #a, a[n]=2*a[(n-1)\a[n-1]]); a

A335898 a(n) = a(floor((n-1)/a(n-1))) + a(floor((n-2)/a(n-2))) with a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5, 4, 5, 6, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 4, 6, 6, 5, 6, 6, 6, 6, 6, 7, 6, 6, 8, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7

Offset: 1

Altug Alkan, following a suggestion from Andrew R. Booker, Jun 29 2020

This sequence is a_1(n) where a_i(n) = Sum_{k=1..i+1} a_i(floor((n-k)/a_i(n-k))) with a_i(n) = 1 for n <= i+1.

Conjecture: This sequence hits every positive integer.

Altug Alkan, Table of n, a(n) for n = 1..10000

Cf. A130535, A283207.

a[1] = a[2] = 1; a[n_] := a[n] = a[Floor[(n-1)/a[n-1]]] + a[Floor[(n-2)/a[n-2]]]; Array[a, 100] (* Amiram Eldar, Jun 29 2020 *)

a=vector(10^2); a[1]=a[2]=1; for(n=3, #a, a[n]=a[(n-1)\a[n-1]]+a[(n-2)\a[n-2]]); a

A258081 Values of k in A071580.

Original entry on oeis.org

1, 1, 1, 1, 2, 10, 12, 10, 21, 25, 70, 670, 239, 2115, 586, 1619, 26800, 2505, 99019, 40903, 285641, 67166, 1852765

Offset: 1

Andrew R. Booker, May 19 2015

The first 23 terms were found using gwnum, and the first 22 have been independently checked using gmp.

Mersenne Forum, A071580

Cf. A061092, A072532, A113334.

terms=12; p=2; for(n=2, terms, q=p+1; while(!ispseudoprime(q), q=q+p); print1(q\p,", "); p=p*q) \\ Serge Batalov, May 19 2015

A216227 Prime numbers that do not appear in the Euclid-Mullin sequence A000946.

Original entry on oeis.org

5, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 61, 67, 71, 73

Offset: 1

Andrew R. Booker, Mar 13 2013

The sequence is known to continue indefinitely, but it is not known whether it is recursively enumerable. Cox and van der Poorten conjectured that it is and gave a method of computing new terms using the known terms of A000946.

A. R. Booker, On Mullin's second sequence of primes, Integers, 12A (2012), article A4.
C. D. Cox and A. J. van der Poorten, On a sequence of prime numbers, Journal of the Australian Mathematical Society 8 (1968), pp. 571-574.
A. A. Mullin, Research Problem 8: Recursive function theory, Bull. Amer. Math. Soc., 69 (1963), 737.
P. Pollack and E. Trevino, The primes that Euclid forgot, 2013.

Cf. A000946 (Euclid-Mullin sequence).

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User: Andrew R. Booker

A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

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A335898 a(n) = a(floor((n-1)/a(n-1))) + a(floor((n-2)/a(n-2))) with a(1) = a(2) = 1.

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A258081 Values of k in A071580.

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PARI

A216227 Prime numbers that do not appear in the Euclid-Mullin sequence A000946.

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