cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A115668 Brilliant numbers (A078972) whose digit reversal is a square.

Original entry on oeis.org

4, 9, 10, 121, 169, 961, 1273, 1843, 10201, 10609, 12769, 16171, 44521, 48361, 48613, 94249, 96721, 106009, 108853, 121879, 129307, 445051, 526567, 613927, 1026169, 1042441, 1062961, 1216609, 1442401, 1692601
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			1843=19*97 is brilliant and 3481=59^2 is a square.

Crossrefs

Cf. A078972, A115667, A115669.

Programs

  • Mathematica
    brilQ[n_]:=Module[{fin=FactorInteger[n]},Total[Transpose[fin][[2]]]==2&& Length[Union[IntegerLength[Transpose[fin][[1]]]]]==1]
brilnos=Select[Range[1700000],brilQ];
Select[brilnos,IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[#]]]]]&]  (* Harvey P. Dale, Feb 06 2011 *)

A115673 Brilliant numbers (A078972) whose digit reversal is a cube.

Original entry on oeis.org

10, 70597, 76121, 211591, 291149, 616571, 7272901, 57337417, 378806833, 789116813, 823405771, 888373133, 1692598807, 1939045681, 4836390103, 15291850411, 33665303431, 37060704397, 44784187919, 46061286319, 52604613989, 52625529791, 52651506241, 57380319289
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			76121=163*467 is brilliant and 12167=23^3.

Links

Crossrefs

Cf. A078972, A115674.

Programs

  • Mathematica
    bnQ[n_]:=Module[{f=Transpose[FactorInteger[n]]},Total[f[[2]]]==2&&Length[Union[ IntegerLength[f[[1]]]]]==1]; Join[{10},Select[Union[ FromDigits[ Reverse[ IntegerDigits[#]]]&/@ (Range[5000]^3)],bnQ]] (* Harvey P. Dale, Jun 12 2014 *)

Extensions

a(7)-a(20) from Donovan Johnson, Mar 10 2010
More terms from Harvey P. Dale, Jun 12 2014

A115675 Brilliant numbers (A078972) whose digit reversal is a powerful(1) number (A001694).

Original entry on oeis.org

4, 9, 10, 121, 169, 869, 961, 1273, 1843, 10201, 10609, 12769, 16171, 44521, 48361, 48613, 70597, 76121, 94249, 96721, 106009, 108853, 121879, 129307, 211591, 255953, 276491, 278699, 291149, 445051, 526567, 613927, 616571, 1026169
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			869 = 11*79 is brilliant and 968 = 2^3*11^2 is powerful.

Links

Crossrefs

Cf. A001694, A078972, A115676.

A115676 Powerful(1) numbers (A001694) whose digit reversal is a brilliant number (A078972).

Original entry on oeis.org

4, 9, 121, 169, 400, 900, 961, 968, 3481, 3721, 4000, 9000, 10201, 12100, 12167, 12544, 12769, 16384, 16900, 17161, 31684, 40000, 79507, 90000, 90601, 94249, 96100, 96721, 96800, 121000, 150544, 169000, 175616, 192200, 194672, 195112
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			968=2^3*11^2 is powerful and 869=11*79 is brilliant.

Links

Crossrefs

Cf. A001694, A078972, A115675.

A115678 Triangular numbers whose digit reversal is a brilliant number (A078972).

Original entry on oeis.org

6, 120, 946, 1540, 7021, 13366, 14365, 15400, 19306, 35245, 72010, 95266, 156520, 179101, 191890, 334153, 341551, 913276, 925480, 933661, 946000, 1008910, 1030330, 1131760, 1383616, 1945378, 3066526, 3156328, 3308878, 3584503
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			946=T(43) and 649=11*59 is brilliant.

Links

Crossrefs

Cf. A078972, A115677.

Programs

  • Mathematica
    bnoQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},PrimeOmega[n] == 2 && IntegerLength[f[[1]]]==IntegerLength[f[[2]]]]; Select[Accumulate[Range[3000]], bnoQ[FromDigits[Reverse[IntegerDigits[#]]]]&] (* Harvey P. Dale, Feb 21 2013 *)

A083285 Numbers n such that n and n+4 are both brilliant numbers (A078972).

Original entry on oeis.org

6, 10, 21, 319, 403, 529, 667, 799, 1003, 1513, 1537, 2623, 2809, 4183, 16459, 23707, 24613, 31309, 34117, 35179, 35653, 37399, 37669, 39913, 40723, 43357, 46243, 46513, 49183, 50689, 53293, 55417, 55747, 56257, 59287, 60547, 61069, 61093
Offset: 1

Views

Author

Jason Earls, Jun 03 2003

Keywords

Examples

			a(5)=403 because 403=13*31 and 407=11*37.

Crossrefs

Cf. A078972.

A085648 Brilliant numbers (A078972) whose digital sum is also brilliant.

Original entry on oeis.org

4, 6, 9, 15, 121, 253, 361, 437, 451, 473, 527, 671, 703, 799, 851, 901, 923, 979, 1003, 1027, 1067, 1081, 1139, 1157, 1207, 1247, 1261, 1333, 1513, 1517, 1643, 1711, 2183, 2291, 2701, 2813, 3007, 3403, 3551, 3589, 3713, 4307, 4399, 4489, 5041, 5063, 5767
Offset: 1

Views

Author

Amarnath Murthy, Jason Earls, Jul 11 2003

Keywords

Examples

			7470269 is a term because 7470269 = 1249*5981 and 7+4+7+0+2+6+9 = 35 = 5*7.

Links

Crossrefs

Cf. A078972.

Programs

  • Maple
    isbril:= proc(n) local F;
  F:= ifactors(n)[2];
  (nops(F)=1 and F[1][2]=2) or (nops(F)=2 and F[1][2]=1 and F[2][2]=1 and ilog10(F[1][1])=ilog10(F[2][1]))
end proc:
R:= NULL:
for d from 1 to 2 do
  if d = 1 then P:= [2,3,5,7]
  else P:= select(isprime, [seq(i,i=10^(d-1)+1..10^d-1,2)])
  fi;
  R:= R, op(sort(select(t -> isbril(convert(convert(t,base,10),`+`)), [seq(seq(P[i]*P[j],j=1..i),i=1..nops(P))])))
od:
R; # Robert Israel, Nov 24 2020

Extensions

Offset changed by Robert Israel, Nov 24 2020

A115655 Both n and the reverse of n are brilliant numbers (A078972).

Original entry on oeis.org

4, 6, 9, 121, 143, 169, 187, 319, 323, 341, 737, 767, 781, 913, 949, 961, 979, 989, 1273, 1343, 1691, 1843, 1961, 3431, 3481, 3721, 10201, 10807, 11413, 12769, 13231, 15049, 15151, 15251, 15347, 15707, 15857, 16171, 16837, 16867, 17161
Offset: 1

Views

Author

Giovanni Resta, Jan 28 2006

Keywords

Examples

			11413=101*113 and 31411=101*311.

Crossrefs

Cf. A078972, A115656, A085751.

A115663 Prime numbers whose digit reversal is a brilliant number (A078972).

Original entry on oeis.org

41, 53, 109, 137, 163, 193, 307, 317, 349, 397, 773, 977, 997, 1051, 1093, 1171, 1297, 1307, 1451, 1553, 1621, 1721, 1801, 1861, 1951, 3001, 3041, 3323, 3331, 3361, 3461, 3491, 3593, 3631, 3671, 3673, 3701, 3923, 7001, 7151, 7213, 7283
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			997 is prime and 799=17*47 is brilliant.

Crossrefs

Cf. A078972, A115664.

Programs

  • Mathematica
    brilQ[n_]:=Module[{fin=FactorInteger[n]},Total[Transpose[fin][[2]]]==2 && Length[Union[IntegerLength[Transpose[fin][[1]]]]]==1]; Select[Prime[ Range[1000]],brilQ[FromDigits[Reverse[IntegerDigits[#]]]]&] (* Harvey P. Dale, Jun 08 2013 *)

A115664 Brilliant numbers (A078972) whose digit reversal is a prime number.

Original entry on oeis.org

14, 35, 361, 377, 391, 703, 713, 731, 779, 793, 799, 901, 943, 1003, 1007, 1073, 1081, 1139, 1147, 1159, 1189, 1261, 1271, 1333, 1349, 1363, 1369, 1403, 1457, 1501, 1517, 1537, 1541, 1591, 1633, 1643, 1649, 1681, 1711, 1739, 1763, 1829
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			799=17*47 is brilliant and 997 is prime.

Crossrefs

Cf. A078972, A115663.
Previous Showing 11-20 of 88 results. Next

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