STATUS
proposed
approved
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Revision History for A133198
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Triangular numbers such that moving the last digit to the front produces a square.
(history; published version)
(history; published version)
STATUS
editing
proposed
STATUS
editing
proposed
NAME
Triangular numbers such that moving the last digit to the front produces a square number.
EXAMPLE
3240 is a triangular number, 0324 is a square number - hence , 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
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
DATA
1, 10, 3240, 464166, 1043290, 5740966, 335936160, 428264011, 3529890253, 4015289691, 108170400250, 821266581691, 2216062991691, 34830532944360, 2453718234672253, 6017966241009003, 11215323437683690, 214486304402280015, 446417240103777645, 1792095001020995616
LINKS
Giovanni Resta, <a href="/A133198/b133198.txt">Table of n, a(n) for n = 1..100</a>
CROSSREFS
Cf. A133197.
EXTENSIONS
a(20) from Giovanni Resta, May 11 2016
STATUS
approved
editing
AUTHOR
_Tanya Khovanova (tanyakh(AT)yahoo.com), _, Oct 09 2007
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 (deutsch(AT)duke.poly.edu), _, Oct 17 2007
EXTENSIONS
More terms from _Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Oct 17 2007