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

%I A261696 #76 Mar 18 2018 04:45:58
%S A261696 1,7,689,6797,67984832,6798483348333332,
%T A261696 8455610150480042707742277762479,
%U A261696 707328322040172689545426423113211907561874137758547957769721082
%N A261696 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 17-gonal: (15n^2 - 13n)/2.
%C A261696 From _Chai Wah Wu_, Mar 16 2018: (Start)
%C A261696 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 A261696 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 A261696 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 A261696 (End)
%H A261696 Chai Wah Wu, <a href="/A261696/b261696.txt">Table of n, a(n) for n = 1..11</a>
%H A261696 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>
%H A261696 Chai Wah Wu, <a href="/A261696/a261696.txt">terms < 10^70000 to illustrate the pattern observed (see comments)</a>
%e A261696 1, 17, 17689, 176896797 are 17-gonal.
%o A261696 (PARI) heptadecagonal(n)=ispolygonal(n, 17)
%o A261696 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 A261696 Cf. A051671, A051869 (17-gonal numbers), A061109, A061110, A264733, A264738, A264776, A264777, A264842, A264848, A264849, A264804.
%K A261696 nonn,base
%O A261696 1,2
%A A261696 _Anders Hellström_, Nov 26 2015
%E A261696 a(6)-a(8) from _Chai Wah Wu_, Mar 16 2018