A264733 -id:A264733 - cp's OEIS frontend

A264848 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 19-gonal: (17n^2 - 15n)/2.

1, 9, 224, 631909, 58000804596, 61688194098028272863216, 2514637794509678630513616176470588235294117671, 941048382372874985200592647058823529411764708485294117647058823529411764705882352941176469

Offset: 1

Anders Hellström, Nov 26 2015

			1, 19, 19224, 19224631909 are 19-gonal.

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

Cf. A051671, A051871 (19-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264804, A264842, A264849.

enneadecagonal(n)=ispolygonal(n, 19)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!enneadecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))

a(5)-a(8) from Chai Wah Wu, Mar 16 2018

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

Original entry on oeis.org

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

Offset: 1

Anders Hellström, Nov 26 2015

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)

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

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)

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

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)))

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

A264804 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 11-gonal: (9n^2 - 7n)/2.

Original entry on oeis.org

1, 1, 526, 64095, 21420730041, 4528059468080555555556, 3834345160635370971474665069772601398563211, 100751687713984558500838936986634939491022212000570658953744730444103042117925197608458

Offset: 1

Anders Hellström, Nov 25 2015

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

Cf. A051671, A051682 (11-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264842, A264848, A264849.

hendecagonal(n)=ispolygonal(n,11)
first(m)=my(v=vector(m),s="");s="1";print1(1, ", ");for(i=2,m,n=1;while(!hendecagonal(eval(concat(s,Str(n)))),n++);print1(n, ", ");s=concat(s,Str(n)))

a(5)-a(8) from Chai Wah Wu, Mar 16 2018

A264842 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 13-gonal: (11n^2 - 9n)/2.

Original entry on oeis.org

1, 3, 36, 54765, 123152388, 374848814886363636, 85794018663817263665487289502938826, 107072047880615405294526336549204869795454545454545454545454545454545466

Offset: 1

Anders Hellström, Nov 26 2015

			1, 13, 1336, 133654765 are 13-gonal.

Jon E. Schoenfield, Table of n, a(n) for n = 1..11
Wikipedia, Polygonal number

Cf. A051671, A051865 (13-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264848, A264849, A264804.

tridecagonal(n)=ispolygonal(n, 13)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!tridecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))

More terms from Jon E. Schoenfield, Nov 27 2015

A264849 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 23-gonal: (21n^2 - 19n)/2.

Original entry on oeis.org

1, 30, 648, 6701456, 72020220595275, 970458695858595792221157266, 3377345920936319088412440649783459968197698452784332095, 7477788200541027929765479736500643733301085903714718188060185368351929896324223859775571543015918781111399506

Offset: 1

Anders Hellström, Nov 26 2015

			1, 130, 130648 are 23-gonal.

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

Cf. A051671, A051875 (23-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264842, A264848, A264804.

icositrigonal(n)=ispolygonal(n, 23)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!icositrigonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))

a(5)-a(8) from Chai Wah Wu, Mar 15 2018

cp's OEIS Frontend

A264848 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 19-gonal: (17n^2 - 15n)/2.

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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.

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A264804 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 11-gonal: (9n^2 - 7n)/2.

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A264842 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 13-gonal: (11n^2 - 9n)/2.

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A264849 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 23-gonal: (21n^2 - 19n)/2.

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PARI

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