%I #76 Mar 18 2018 04:45:58

%S 1,7,689,6797,67984832,6798483348333332,

%T 8455610150480042707742277762479,

%U 707328322040172689545426423113211907561874137758547957769721082

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

%C From _Chai Wah Wu_, Mar 16 2018: (Start)

%C 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...

%C 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.

%C 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.

%C (End)

%H Chai Wah Wu, <a href="/A261696/b261696.txt">Table of n, a(n) for n = 1..11</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>

%H Chai Wah Wu, <a href="/A261696/a261696.txt">terms < 10^70000 to illustrate the pattern observed (see comments)</a>

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

%o (PARI) heptadecagonal(n)=ispolygonal(n, 17)

%o 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)))

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

%K nonn,base

%O 1,2

%A _Anders Hellström_, Nov 26 2015

%E a(6)-a(8) from _Chai Wah Wu_, Mar 16 2018