A261696 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 17-gonal: (15n^2 - 13n)/2.

1, 7, 689, 6797, 67984832, 6798483348333332, 8455610150480042707742277762479, 707328322040172689545426423113211907561874137758547957769721082

Offset

1,2

Comments

From Chai Wah Wu, Mar 16 2018: (Start)

There are some interesting patterns observed in the terms. Terms a(5), a(6), a(9), a(10), a(11), a(12), ... share the same prefix of 6798483...

From terms a(n) for n > 5, there seems to a pattern of how they are constructed from previous terms. a(6) is formed by inserting 3483...3 between the penultimate digit and the last digit of a(5). Then a(7) and (8) do not follow this pattern.

The digits of a(9) and a(6) match until the last digit of a(6). Next, a(10), a(11) and (12) are formed from a(9), a(10) and a(11) resp. by inserting 3483...3. Then this pattern is interrupted by a(13) and a(14), and continue again for a(15) ..., etc.

(End)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..11

Wikipedia, Polygonal number

Chai Wah Wu, terms < 10^70000 to illustrate the pattern observed (see comments)

Example

1, 17, 17689, 176896797 are 17-gonal.

Prog

(PARI) heptadecagonal(n)=ispolygonal(n, 17)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!heptadecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))

Crossrefs

Cf. A051671, A051869 (17-gonal numbers), A061109, A061110, A264733, A264738, A264776, A264777, A264842, A264848, A264849, A264804.

Sequence in context: A038803 A144957 A163016 * A174855 A186160 A129291

Adjacent sequences: A261693 A261694 A261695 * A261697 A261698 A261699

Keyword

nonn,base

Author

Anders Hellström, Nov 26 2015

Extensions

a(6)-a(8) from Chai Wah Wu, Mar 16 2018

Status

approved