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User: Tim Peters

Tim Peters has authored 2 sequences.

A368161 a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.

1, 25, 441, 100, 169, 289, 121, 2395417249

Offset: 1

J. Stauduhar and Tim Peters, Dec 14 2023

It is conjectured that m always exists.
The present state of knowledge (with ? for unknown entries) is:
1, 25, 441, 100, 169, 289, 121, 2395417249, ?, 15386237159377984, 676, 232324, ?, ?, ?, 64866916, 3721, 3622354596, 279936, ?, ?, 41152225, 29929, 2137444, ?, 11526025, 97969, 9922500, ?, 978626089, ?, 347151424, ?
Known solutions < 10^12 from J. Stauduhar. All others from Tim Peters.

			128 + 144 + 169 = 441, and 441 is the first perfect power that is the sum of three consecutive perfect powers, so a(3) = 441.

J. Stauduhar, 3772 known solutions.

Cf. A001597.

A099053 a(n) is the smallest number of 1s and 2s that are needed to construct n using any number of +, -, *, ^ signs but not allowing concatenation of digits.

Original entry on oeis.org

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

Offset: 1

Tim Peters (tim.one(AT)comcast.net), Nov 14 2004

nonn

Subexpressions can be grouped as needed; equivalently, any number of parentheses can be used in the expression.
Yet another definition of the complexity of a number.
It can be assumed that no subexpression can be <= 0. The only way to generate a negative value is to take a-b with a < b; taking b-a instead gives the absolute value of this expression. For any further number generated using the negative value, the absolute value of that number is obtainable using the absolute value of the subexpression(s). Generating an intermediate zero is useless. - Franklin T. Adams-Watters, Jul 29 2011

			1 = 1, so has complexity 1.
2 = 2, so has complexity 1.
3 = 1+2, so has complexity 2.
4 = 2+2 = 2*2 = 2^2, so has complexity 2.
5 = 2+1+2, so has complexity 3.
...
16 = 2^2^2, so has complexity 3.

David Consiglio, Jr., Table of n, a(n) for n = 1..90
David Consiglio, Jr., Calculations and upper bounds for values through a(200)
Index to sequences related to the complexity of n

Positions of records are given in A060274.

a(35) onwards from David Consiglio, Jr., Oct 19 2023

cp's OEIS Frontend

User: Tim Peters

A368161 a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.

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