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

1,1

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.

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A000217, A069567, A072274, A075093.

Sequence in context: A215998 A186606 A227711 * A254025 A254018 A254892

Adjacent sequences: A247302 A247303 A247304 * A247306 A247307 A247308

Keyword

nonn,base

Author

K. D. Bajpai, Sep 11 2014

Status

approved