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

Author

Anders Hellström, Nov 26 2015

Keywords

• nonn
• base

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)

Examples

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

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)

Crossrefs

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

Programs

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)))

Extensions

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