A133198 Triangular numbers such that moving the last digit to the front produces a square.

1, 10, 3240, 464166, 1043290, 5740966, 335936160, 428264011, 3529890253, 4015289691, 108170400250, 821266581691, 2216062991691, 34830532944360, 2453718234672253, 6017966241009003, 11215323437683690, 214486304402280015, 446417240103777645, 1792095001020995616

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..100

Example

3240 is a triangular number, 0324 is a square, so 3240 belongs to this sequence.

Maple

a:=proc(n) local n2, L: n2:=convert((1/2)*n*(n+1), base, 10): L:=nops(n2): if type(sqrt((1/20)*n*(n+1)-(1/10)*n2[1]+n2[1]*10^(L-1)), integer)=true then (1/2)*n*(n+1) else end if end proc: seq(a(n), n=1..10^7); # Emeric Deutsch, Oct 17 2007

Mathematica

Select[Table[n(n + 1)/2, {n, 1000000}], IntegerQ[Sqrt[ FromDigits[ Prepend[Drop[IntegerDigits[ # ], -1], Last[IntegerDigits[ # ]]]]]] &]

Crossrefs

Cf. A000217, A000290, A133197.

Sequence in context: A320307 A225764 A243008 * A292443 A001329 A007101

Adjacent sequences: A133195 A133196 A133197 * A133199 A133200 A133201

Keyword

base,nonn

Author

Tanya Khovanova, Oct 09 2007

Extensions

More terms from Emeric Deutsch, Oct 17 2007

Offset corrected and a(15)-a(19) from Donovan Johnson, Jan 31 2011

a(20) from Giovanni Resta, May 11 2016

Status

approved