A247305 The smaller of two consecutive triangular numbers which are permutations of each other.

404550, 2653056, 3643650, 5633046, 6413571, 10122750, 10656036, 13762881, 19841850, 26634051, 32800950, 47848653, 56769840, 71634465, 89184690, 103672800, 137108520, 317053971, 345069585, 392714325, 408508236, 440762895, 508948560, 598735710, 718830486, 825215625

Offset: 1

Author

K. D. Bajpai, Sep 11 2014

Keywords

• nonn
• base

Comments

All the terms in sequence are congruent to 0 mod 9.

It appears that the digital root (repeated sum of digits) of the index +1 of a(n) in A000217 is 9 for each n>=1.o 0 mod 9. For example, 404550 = A000217(899), and 899+1 = 900 has digital root 9.

Examples

			a(1) = 404550 is in the sequence because {404550 and 405450} are a pair of consecutive triangular numbers having exactly the same digits.
a(2) = 2653056 is in the sequence because {2653056 and 2655360} are two consecutive triangular numbers having exactly the same digits.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..13000

Crossrefs

Cf. A000217, A069567, A072274, A075093.

Programs

Mathematica

A247305 = {}; a = {1}; b = {2}; Do[t1 = n*(n + 1)/2; t2 = (n - 1)*(n - 1 + 1)/2; b = Sort[IntegerDigits[t1]]; If[a == b, AppendTo[A247305, t2]]; a = b, {n, 2, 7*10^4}]; A247305

PARI

lista(nn) = {for (n=1, nn, dt = vecsort(digits(t=n*(n+1)/2)); dnt = vecsort(digits((n+1)*(n+2)/2)); if (dt == dnt, print1(t, ", ")););} \\ Michel Marcus, Sep 13 2014