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# User talk:M. F. Hasler/Ranges

Here I list "ranges" of sequences, usually submitted as "bulk", often with insufficient complementary information (missing link to index and/or crossrefs to start or end of range and other relevant sequences, and mostly no formula or interesting program). In most cases I tried to provide this complementary information. In some cases I completed the missing seq's in the series, and linked the existing ones among each other.

## Contents

### n-k and k-n, k=1 .. 40

n-k: A023443, ..., A023482 (k=1..40);

Here I added xrefs between the two, formula for recurrence, g.f., linking n-k to k-n, and PARI code.

### n^k and k^n

Powers of given k: A000079 (2^n), A000244 (3^n), A000302 (4^n), A000351 (5^n), A000400 (6^n), A000420 (7^n),

- (ranges): A001019 (9^n), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009992 (powers of 48),
- (finish): A087752 (powers of 49), A165800 (powers of 50), A159991 (powers of 60).

Given powers of n: squares, cubes, ... (to be completed).

Partial sums of powers, i.e., (k^n-1)/(k-1):

- A000225 (k=2), A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275 (k=10), A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108 (k=20), A218724-A218734 (k=21..31), A132469, A218736-A218753 (k=33..50), A133853 (k=64), A094028 (k=100), A218723 (k=256).

### circular base b numbers with adjacent digits differing by less than x

A125373 and neighbours (members of large /Ranges!): They have a rational g.f. and are recurrent sequences. GF + link to /index/Rec#... should be added. Note, they seem to be first differences of sequences 6^n-5^n = A005062 etc. but this is only true for the first few membres! - MFH, May 03 2015

### n-th root of x

(Decimal expansion of ...): A011200 - A011519 is another huge range of sequences of this "bulk" type.

- (15 (n=6..20) * 16 (x=5..20) + 80 (n=x=20..100) ~ 320)

- x = 5, n = 6 .. 20: A011200 ... A011214
- x = 6, n = 6 .. 20: A011215 ... A011229
- x = 7, n = 6 .. 20: A011230 ... A011244
- x = 8, n = 6 .. 20: A011245 ... A011259
- x = 9, n = 6 .. 20: A011261 ... A011273 : Decimal expansion of 7, 9, ..., 19th root of 9. (Only odd n, only every other A-number.)
- x = 10, n = 6 .. 20: A011275 ... A011289 : Decimal expansion of 6th ... 20th root of 10.
- x = 11, n = 6 .. 20: A011290 ... A011304 : Decimal expansion of 6th ... 20th root of 11.
- x = 12, n = 6 .. 20: A011305 ... A011319 : Decimal expansion of 6th ... 20th root of 12.
- x = 13 ; n = 6 ... 20: A011320 ... A011334 : Decimal expansion of 6th ... 20th root of 13.
- x = 14 ; n = 6 ... 20: A011335 ... A011349 : Decimal expansion of 6th ... 20th root of 14.
- x = 15 ; n = 6 ... 20: A011350 ... A011364 : Decimal expansion of 6th ... 20th root of 15.
- x = 16 ; n = 6 ... 20: A011365 ... A011379 : Decimal expansion of 6th ... 20th root of 16.
- x = 17 ; n = 6 ... 20: A011380 ... A011394 : Decimal expansion of 6th ... 20th root of 17.
- x = 18 ; n = 6 ... 20: A011395 ... A011409 : Decimal expansion of 6th ... 20th root of 18.
- x = 19 ; n = 6 ... 20: A011410 ... A011424 : Decimal expansion of 6th ... 20th root of 19.
- x = 20 ; n = 6 ... 20: A011425 ... A011439 : Decimal expansion of 6th ... 20th root of 20.

For n = 20 .. 100, decimal expansion of the n-th root of n:

- x = n = 20-th ... 100-th root of x = n : A011439 ... A011449 ... A011459 ... A011469 ... A011479 ... A011489 ... A011499 ... A011509 ... A011519.

### ...

(...more to come...)