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
See
A066528 for a different version.
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
153 and 351 are both triangular.
-
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]]]
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
153 and 351 are both triangular.
-
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 *)
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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
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
565187=P(614) and 781565=P(722), where P(k) = k*(3*k-1)/2 is the k-th pentagonal number.
-
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
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
BinaryReverse(120) = 15, DecimalReverse(120) = 21. Because 120, 15 and 21 are triangular numbers, 120 is in the sequence.
-
#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
Showing 1-6 of 6 results.
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