Less Is Cor

The splendor falls on castle walls
    And snowy summits old in story;
The long light shakes across the lakes,
    And the wild cataract leaps in glory.
Blow, bugle, blow, set the wild echoes flying,
Blow, bugle; answer, echoes, dying, dying, dying.

O, hark, O, hear! how thin and clear,
    And thinner, clearer, farther going!
O, sweet and far from cliff and scar
    The horns of Elfland faintly blowing!
Blow, let us hear the purple glens replying,
Blow, bugles; answer, echoes, dying, dying, dying.

O love, they die in yon rich sky,
    They faint on hill or field or river;
Our echoes roll from soul to soul,
    And grow forever and forever.
Blow, bugle, blow, set the wild echoes flying,
And answer, echoes, answer, dying, dying, dying.

• From Tennyson’s The Princess (1847)

I’m a Beweaver

Here are some examples of what I call woven sums for sum(n1..n2), where the digits of n1 are interwoven with the digits of n2:

1599 = sum(19..59) = 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56
2716 = sum(21..76)
159999 = sum(199..599)
275865 = sum(256..785)
289155 = sum(295..815)
15050747 = sum(1004..5577)
15058974 = sum(1087..5594)
15999999 = sum(1999..5999)
39035479 = sum(3057..9349)


In other words, the digits of n1 occupy digit-positions 1,3,5… and the digits of n2 occupy dig-pos 2,4,6…

But I can’t find woven sums where the digits of n2 are interwoven with the digits of n1, i.e. the digits of n2 occupy dig-pos 1,3,5… and the digits of n1 occupy dig-pos 2,4,6… Except when n1 has fewer digits than n2, e.g. 210 = sum(1..20).


Elsewhere Other-Accessible…

Nuts for Numbers — a look at numbers like 2772 = sum(22..77) and 10470075 = sum(1075..4700).