A084385 -id:A084385 - cp's OEIS frontend

A111244 Partial sums of A084385.

1, 3, 7, 10, 17, 22, 31, 37, 45, 56, 69, 79, 91, 106, 123, 137, 153, 172, 193, 211, 231, 254, 279, 301, 325, 352, 381, 407, 435, 466, 499, 529, 561, 596, 633, 667, 703, 742, 783, 821, 861, 904, 949, 991, 1035, 1082, 1131, 1177, 1225, 1276, 1329, 1379, 1431, 1486, 1543

Offset: 1

N. J. A. Sloane, Oct 31 2005

nonn

a(n+1) = a(n) + (smallest number coprime with a(n) and not already added). - Reinhard Zumkeller, Aug 15 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A084385, A089781.

a111244 n = a111244_list !! (n-1)
a111244_list = scanl1 (+) a084385_list
-- Reinhard Zumkeller, Aug 15 2015

A261351 Inverse permutation to A084385.

Original entry on oeis.org

1, 2, 4, 3, 6, 8, 5, 9, 7, 12, 10, 13, 11, 16, 14, 17, 15, 20, 18, 21, 19, 24, 22, 25, 23, 28, 26, 29, 27, 32, 30, 33, 31, 36, 34, 37, 35, 40, 38, 41, 39, 44, 42, 45, 43, 48, 46, 49, 47, 52, 50, 53, 51, 56, 54, 57, 55, 60, 58, 61, 59, 64, 62, 65, 63, 68, 66

Offset: 1

Reinhard Zumkeller, Aug 16 2015

nonn

-4 <= a(n) - A084385(n) <= 3;
for n > 4: a(n) != A084385(n);
for n > 7: a(n) >= A084385(n) - 3.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A084385.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a261351 = (+ 1) . fromJust . (`elemIndex` a084385_list)

A357735 a(1)=1, a(2)=2. Thereafter a(n+1) is least k != partial sum s(n) which has not occurred earlier, such that gcd(k, s(n)) > 1.

Original entry on oeis.org

1, 2, 6, 3, 4, 8, 9, 11, 10, 12, 14, 5, 15, 16, 18, 20, 7, 21, 13, 24, 27, 22, 26, 28, 23, 25, 30, 32, 33, 31, 34, 35, 40, 44, 55, 36, 37, 39, 17, 42, 45, 38, 46, 48, 50, 19, 57, 52, 41, 62, 43, 54, 56, 58, 60, 64, 51, 63, 66, 49, 70, 77, 68, 69, 72, 75, 74, 76

Offset: 1

David James Sycamore, Oct 11 2022

nonn

It follows from the definition that if s(n) is prime then a(n+1) = 2*s(n). This happens only once in the sequence, when a(3)=6, following s(2)=3. For all n > 2 s(n) is composite. Conjectured to be a permutation of the positive integers (primes not in natural order).

			Since a(1)=1 and a(2)=2, we have s(2)=3, then a(3) is 6, the smallest unused term sharing a divisor with 3.

Michael De Vlieger, Table of n, a(n) for n = 1..16384
Michael De Vlieger, Log-log scatterplot of a(n) n = 1..2^17, labeling records in red, local minima in blue, and highlighting prime terms in green.

Cf. A064413, A084385, A347113, A351743.

nn = 2^16; c[] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = s = 3; Do[k = u; While[Nand[! c[k], ! CoprimeQ[k, s], k != s], k++]; Set[{a[n], c[k]}, {k, True}]; s += k; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* _Michael De Vlieger, Oct 11 2022 *)

A374950 Sequence starting with 2, where the next term is the lowest new integer which is greater than 1 and coprime with the sum of all previous terms.

Original entry on oeis.org

2, 3, 4, 5, 9, 6, 7, 11, 8, 12, 10, 13, 17, 14, 15, 19, 16, 20, 18, 21, 27, 22, 23, 25, 26, 24, 28, 29, 33, 30, 31, 35, 32, 36, 34, 37, 41, 38, 39, 43, 40, 44, 42, 45, 49, 46, 47, 53, 48, 50, 51, 55, 52, 56, 54, 57, 61, 58, 59, 67, 60, 62, 64, 63, 65, 68, 66

Offset: 1

Declan Boushy, Jul 24 2024

nonn

Cf. A084385 (starting with 1).

a={2}; s=2;For[n=2, n<=67, n++,k=2; While[GCD[k,s]!=1||MemberQ[a,k], k++]; s+=k; AppendTo[a,k]]; a (* Stefano Spezia, Jul 25 2024 *)

More terms from Pontus von Brömssen, Jul 25 2024

cp's OEIS Frontend

A111244 Partial sums of A084385.

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A261351 Inverse permutation to A084385.

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A357735 a(1)=1, a(2)=2. Thereafter a(n+1) is least k != partial sum s(n) which has not occurred earlier, such that gcd(k, s(n)) > 1.

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A374950 Sequence starting with 2, where the next term is the lowest new integer which is greater than 1 and coprime with the sum of all previous terms.

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Mathematica

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