A337097 Infinite sum of the odd numbers, compacted (see the Comments line for an explanation).

4, 12, 20, 28, 57, 203, 76, 129, 371, 124, 201, 219, 237, 623, 505, 327, 2489, 1099, 332, 865, 543, 1337, 2743, 452, 1165, 723, 1757, 1315, 813, 831, 849, 2051, 604, 921, 939, 10757, 1915, 5213, 2095, 3017, 2215, 5993, 2395, 1461, 6539, 2605, 17267, 2965, 1803, 1821, 1839, 1857, 12179, 1324, 8801

Offset

1,1

Comments

When the successive terms of the present sequence are expressed as the sum of k>1 consecutive odd numbers and added, the end result will be 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17...... (conjectured to extend ad infinitum).

This is the lexicographically earliest sequence of distinct positive terms with this property.

The equivalent sequence with sums of consecutive even numbers is simply A336897 where every term is doubled.

Links

Table of n, a(n) for n=1..55.

Example

The 1st term is 4 and 4 = 1+3.
The 2nd term is 12 and 12 = 5+7.
The 3rd term is 20 and 20 = 9+11.
The 4th term is 28 and 28 = 13+15.
The 5th term is 57 and 57 = 17+19+21; etc.
(The 5th term is NOT 36 as 36 can be expressed as the sum of k>1 consecutive odd numbers in more than one way: 36 = 17+19 and 36 = 1+3+5+7+9+11).

Crossrefs

Cf. A336897, A337094.

Sequence in context: A062876 A301098 A301267 * A238836 A085039 A267194

Adjacent sequences: A337094 A337095 A337096 * A337098 A337099 A337100

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 15 2020

Status

approved