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.

Showing 1-6 of 6 results.

A069673 Nonpalindromic triangular numbers whose digit reversal is also a triangular number (possibly with fewer digits).

Original entry on oeis.org

10, 120, 153, 190, 300, 351, 630, 820, 17578, 87571, 156520, 180300, 185745, 547581, 557040, 678030, 1461195, 1851850, 5911641, 6056940, 12145056, 12517506, 16678200, 56440000, 60571521, 65054121, 157433640, 188267310, 304119453, 354911403, 1261250200
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Crossrefs

See A066528 for a different version.

Extensions

More terms from Jason Earls, Jun 07 2002
a(27)-a(31) from Giovanni Resta, Jun 20 2015

A066528 Non-palindromic triangular numbers whose reverse is a triangular number with the same number of digits.

Original entry on oeis.org

153, 351, 17578, 87571, 185745, 547581, 1461195, 5911641, 12145056, 12517506, 60571521, 65054121, 304119453, 354911403, 1775275491, 1945725771, 10246462281, 17990863516, 18226464201, 35615002605, 50620051653, 61536809971, 1222080857271, 1664224065406
Offset: 1

Views

Author

Erich Friedman, Jan 08 2002

Keywords

Examples

			153 and 351 are both triangular.
		

Crossrefs

See A069673 for another version.

Programs

  • Mathematica
    dtn[L_] := Fold[10#1+#2&, 0, L]; tritest[n_] := Module[{t}, t=Floor[N[Sqrt[2n]]]; 2n==t(t+1)]; A={}; For[i=1, i>0, i++, t=i(i+1)/2; If[tritest[tt=dtn[Reverse[IntegerDigits[t]]]]&&Mod[t, 10]>0&&t=!=tt, AppendTo[A, t]; Print[A]]]

Extensions

a(22)-a(24) from Giovanni Resta, Jun 20 2015

A066569 Triangular numbers whose reverse is also triangular.

Original entry on oeis.org

1, 3, 6, 55, 66, 153, 171, 351, 595, 666, 3003, 5995, 8778, 15051, 17578, 66066, 87571, 185745, 547581, 617716, 828828, 1269621, 1461195, 1680861, 3544453, 5073705, 5676765, 5911641, 6295926, 12145056, 12517506, 35133153, 60571521
Offset: 1

Views

Author

Erich Friedman, Jan 08 2002

Keywords

Comments

Numbers ending in 0 are not included. - Harry J. Smith, Mar 06 2010

Examples

			153 and 351 are both triangular.
		

Crossrefs

Programs

  • Mathematica
    dtn[L_] := Fold[10#1+#2&, 0, L] tritest[n_] := Module[{t}, t=Floor[N[Sqrt[2n]]]; 2n==t(t+1)] A={}; For[i=1, i>0, i++, t=i(i+1)/2; If[tritest[dtn[Reverse[IntegerDigits[t]]]]&&Mod[t, 10]>0, AppendTo[A, t]; Print[A]]]
    Select[Accumulate[Range[12000]],Last[IntegerDigits[#]]!=0&&OddQ[Sqrt[1+ 8*FromDigits[Reverse[IntegerDigits[#]]]]]&] (* Harvey P. Dale, Jun 04 2015 *)
  • PARI
    Rev(x)= { local(d, r=0); while (x>0, d=x%10; x\=10; r=r*10 + d); return(r) } { n=0; for (m=1, 10^10, t=m*(m + 1)/2; if (t%10 == 0, next); if (issquare(8*Rev(t) + 1), write("b066569.txt", n++, " ", t); if (n==100, return)) ) } \\ Harry J. Smith, Mar 08 2010

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Mar 06 2010

A115657 Both k and the reverse of k are pentagonal numbers (A000326).

Original entry on oeis.org

0, 1, 5, 22, 210, 287, 782, 1001, 2882, 7740, 15251, 77180, 565187, 720027, 781565, 7081807, 7451547, 26811862, 54177145, 206489067, 246214610, 760984602, 1050660501, 1085885801, 1528888251, 2642326276, 2911771192, 6726232462, 24375132126, 62123157342
Offset: 1

Views

Author

Giovanni Resta, Jan 28 2006

Keywords

Examples

			565187=P(614) and 781565=P(722), where P(k) = k*(3*k-1)/2 is the k-th pentagonal number.
		

Crossrefs

Programs

  • PARI
    lista(nn) = for (n=0, nn, my(P = n*(3*n-1)/2); if (ispolygonal(fromdigits(Vecrev(digits(P))), 5), print1(P, ", "));); \\ Michel Marcus, May 22 2022

Extensions

0 and additional terms from Jon E. Schoenfield, May 22 2022

A225884 Triangular numbers whose binary and decimal reversals are also triangular numbers.

Original entry on oeis.org

0, 1, 3, 6, 120, 153, 300
Offset: 1

Views

Author

Alex Ratushnyak, May 24 2013

Keywords

Comments

A subsequence of A061455.
a(8), if it exists, is > triangular(10^11) > 5*10^21. - Lars Blomberg, Jan 11 2016

Examples

			BinaryReverse(120) = 15, DecimalReverse(120) = 21. Because 120, 15 and 21 are triangular numbers, 120 is in the sequence.
		

Crossrefs

Programs

  • C
    #include 
    #include 
    #include 
    int isTriangular(unsigned long long a) {
        unsigned long long sr = sqrt(a*2);
        return (sr*(sr+1) == a*2);
    }
    int main() {
      unsigned long long n, tn, t, r;
      for (n = tn = 0; tn < (1ULL<<63); tn += ++n) {
        for (r=0, t=tn; t; t>>=1)  r = r*2 + (t&1);
        if (isTriangular(r)==0) continue;
        for (r=0, t=tn; t; t/=10)  r = r*10 + (t%10);
        if (isTriangular(r)==0) continue;
        printf("%llu, ", tn);
      }
      return 0;
    }

A226035 Prime powers (A025475) whose decimal digit reversal is also a prime power.

Original entry on oeis.org

1, 4, 8, 9, 121, 169, 343, 961, 1331, 10201, 12769, 14641, 94249, 96721, 1030301, 1042441, 1062961, 1216609, 1442401, 1692601, 9066121, 104060401, 121066009, 900660121, 12148668841, 12367886521, 12568876321, 14886684121, 1000422044521, 1002007006009, 1020506060401
Offset: 1

Views

Author

Alex Ratushnyak, May 24 2013

Keywords

Crossrefs

Showing 1-6 of 6 results.