A264848
a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 19-gonal: (17n^2 - 15n)/2.
Original entry on oeis.org
1, 9, 224, 631909, 58000804596, 61688194098028272863216, 2514637794509678630513616176470588235294117671, 941048382372874985200592647058823529411764708485294117647058823529411764705882352941176469
Offset: 1
1, 19, 19224, 19224631909 are 19-gonal.
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)))
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
1, 17, 17689, 176896797 are 17-gonal.
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)))
A264733
a(n) is the smallest number > 1 such that the concatenation a(1)a(2)...a(n) is a perfect power.
Original entry on oeis.org
4, 9, 13, 31556, 4433200001, 7330164793357114944, 364233003001227343654904892703798707409, 30558883460500823396683989630832748682356643682219859233661160618544138815441
Offset: 1
Cf.
A001597(perfect powers),
A051671,
A061109,
A061110,
A261696,
A264738,
A264776,
A264777,
A264804,
A264842,
A264848,
A264849.
-
a[1]:= 4: C:= 4:
for n from 2 to 9 do
looking:= true;
for d from 1 while looking do
L:= 10^d*C + 10^(d-1);
U:= 10^d*C + 10^d - 1;
p:= 1;
while p < ilog2(U) do
p:= nextprime(p);
Lp:= ceil(L^(1/p));
Up:= floor(U^(1/p));
while not (Lp::integer and Up::integer) do
Digits:= 2*Digits;
Lp:= eval(Lp);
Up:= eval(Up);
od;
if Lp <= Up then
Cp:= Lp^p;
a[n]:= Cp - 10^d*C;
C:= Cp;
looking:= false;
break
fi
od
od
od:
seq(a[i],i=1..9); # Robert Israel, Nov 27 2015
-
a = {}; Do[k = 2; While[! Or[# == 1, GCD @@ FactorInteger[#][[All, -1]] > 1] &@ FromDigits@ Flatten@ Join[#, IntegerDigits@ k], k++] &@ Map[IntegerDigits, a]; AppendTo[a, k], {i, 4}]; a (* Michael De Vlieger, Jan 23 2017 *)
-
first(m)=my(s="4"); print1(4, ", "); for(i=2,m,n=1; while(!ispower(eval(concat(s,Str(n)))),n++); print1(n, ", "); s=concat(s,Str(n)))
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
1, 13, 1336, 133654765 are 13-gonal.
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)))
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
1, 130, 130648 are 23-gonal.
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)))
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