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.
a(10) = 4: 1264114621, 1634004361, 5289009825, 6172882716.
a(4) = 3003 = 77*78/2 is the smallest 4-digit palindromic triangular number. a(12) = 0 as no 12-digit palindromic triangular number exists.
a(4) = 77 as 77*78/2 = 3003 is the smallest 4-digit palindromic triangular number. a(12) = 0 as no 12-digit palindromic triangular number exists.
a(4) = 8778 = 132*133/2 is the largest 4-digit palindromic triangular number. a(12) = 0 as no 12-digit palindromic triangular number exists.
a(4) = 132 as 132*133/2 = 8778 is the largest 4-digit palindromic triangular number. a(12) = 0 as no 12-digit palindromic triangular number exists.
palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; t={}; c=0; Do[If[palQ[n*(n+1)/2],c=c+1; If[PrimeQ[n],AppendTo[t,c]]],{n,10^3}]; t (* Jayanta Basu, May 14 2013 *)
ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1 for(k=1,1e9,if(ispal(k*(k+1)/2),n++;if(isprime(k),print1(n", ")))) \\ Charles R Greathouse IV, May 15 2013
a(5)=3003 because 3003 is 77th triangular number and 77 is palindrome.
Select[Table[{n,(n(n+1))/2},{n,10^8}],AllTrue[#,PalindromeQ]&][[;;,2]] (* Harvey P. Dale, Jun 04 2023 *)
5 is a term since 5 = 101_2 is a binary palindromic number and A000217(5) = 5*(5+1)/2 = 15 = 1111_2 is a triangular number and also a binary palindromic number.
Select[Range[0, 10^6], And @@ PalindromeQ /@ IntegerDigits[{#, #*(# + 1)/2}, 2] &]
isok(k) = my(bt=binary(k*(k+1)/2), bk=binary(k)); (bt == Vecrev(bt)) && (bk==Vecrev(bk)); \\ Michel Marcus, Jan 28 2022
from itertools import count, islice def ispal(s): return s == s[::-1] def ok(n): return ispal(bin(n)[2:]) and ispal(bin(n*(n+1)//2)[2:]) print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jan 28 2022
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