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.

A363379 Numbers k such that the sum of the first k terms of A180405 is composite.

Original entry on oeis.org

5, 9, 13, 17, 21, 25, 27, 33, 41, 47, 55, 61, 65, 69, 75, 83, 89, 95, 105, 107, 113, 119, 125, 128, 133, 139, 145, 155, 161, 165, 171, 179, 183, 189, 197, 201, 207, 211, 217, 225, 231, 237, 241, 247, 255, 261, 267, 271, 279, 285, 289, 297, 303, 307, 313, 319, 327, 333, 339, 343, 351
Offset: 1

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Author

Neal Gersh Tolunsky, May 29 2023

Keywords

Comments

The construction in A180405 means terms here cannot be terms there, but do any other numbers never occur there?
Indices of composite terms in A363450 (partial sums of A180405).
a(24)=128 is possibly the only even term in the sequence (checked for 6000 terms).

Links

Crossrefs

Cf. A180405, A363450.

A363450 Partial sums of A180405.

Original entry on oeis.org

2, 3, 7, 13, 16, 23, 31, 41, 52, 67, 79, 97, 111, 127, 149, 173, 192, 223, 251, 271, 294, 331, 367, 397, 423, 457, 486, 521, 563, 601, 641, 673, 712, 757, 809, 853, 907, 953, 1009, 1069, 1112, 1163, 1213, 1277, 1361, 1409, 1458, 1511, 1579, 1637, 1699, 1777, 1847, 1913, 1970
Offset: 1

Views

Author

Neal Gersh Tolunsky, Jun 02 2023

Keywords

Comments

The construction in A180405 means that if n is in A180405, then a(n) is prime. It seems that the converse is also true: if a(n) here is prime, then n is in A180405.
Indices of composite terms are given by A363379.

Links

Crossrefs

Cf. A180405, A363379.

A366170 Lexicographically earliest sequence of distinct positive integers such that for n>1, Sum_{i=1..n, a(i)<=n} a(a(i)) is prime.

Original entry on oeis.org

1, 2, 4, 8, 6, 12, 5, 7, 10, 18, 13, 11, 14, 16, 17, 24, 20, 22, 21, 15, 19, 26, 3, 23, 9, 30, 28, 32, 31, 29, 40, 42, 34, 36, 37, 44, 35, 27, 41, 50, 46, 39, 33, 56, 47, 52, 68, 49, 43, 54, 53, 51, 60, 58, 57, 45, 66, 55, 61, 74, 64, 63, 84, 72, 67, 78, 65, 59, 70, 90, 73, 80
Offset: 1

Views

Author

Neal Gersh Tolunsky, Oct 02 2023

Keywords

Comments

At a new term k, a(n) = k adds a(k) to the current prime sum if k <= n. If n is a term in the sequence among a(1..n-1), then a(n) = k is added. If neither of these conditions is met, the current prime sum remains the same.
If k is even and a(k) odd, then k cannot appear as a(n) = k at any n >= k (otherwise, the intended prime sum will be even, and thus not prime). This means that some even numbers will miss their chance and never appear. 38 is the smallest missing number.
Can it be proved that every odd number appears?

Examples

			At [1,2], the terms at indices i=1 and i=2, namely 1 and 2, sum to 3, a prime.
At [1,2,4], i=4 is not the index of a term in the sequence yet, so the sum remains the same.
At [1,2,4,8], the sum of the terms at i=1,2,4 is a(1)=1 + a(2)=2 + a(4)=8, which is 11, a prime number.

Links

Crossrefs

Cf. A054408, A180405, A359535.
Showing 1-3 of 3 results.

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

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