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A087598
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Define dd(k) = the number formed by concatenating the absolute difference of successive digits of k. Triangular numbers t such that dd(t)= say, r, dd(r) = s and so on Then t,r,s etc. are triangular numbers until a single-digit triangular number (0,1,3,or 6 ) arises. (Triangular number in which the number formed by successive digit difference is also a triangular number at every step which finally ends up in a one-digit triangular number.).
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3
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10, 21, 28, 36, 45, 55, 66, 78, 171, 465, 528, 666, 2211, 4465, 22791, 333336
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Conjecture: Sequence is infinite.
No more terms < 10^12. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
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EXAMPLE
| 528 is a member as dd(528) = 36, dd(36) = 3. 528, 36 and 3 are triangular numbers.
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MATHEMATICA
| trnoQ[n_]:=IntegerQ[(Sqrt[8n+1]-1)/2]; oknQ[n_]:=Module[{ll= NestWhileList[FromDigits[Abs[Differences[IntegerDigits[#]]]]&, n, #>9&]}, Length[ll]>1&&And@@trnoQ/@ll]; Select[Accumulate[Range[ 2000000]], oknQ] (* From Harvey P. Dale, May 15 2011 *)
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PROG
| (PARI) dd(k)={ local(kshf, res, dig, odig, p) ; kshf=k ; res=0 ; odig=kshf % 10 ; p=0 ; while(kshf>9, kshf=floor(kshf/10) ; dig=kshf % 10 ; res += 10^p*abs(dig-odig) ; odig=dig ; p++ ; ) ; return(res) ; } isA000217(n)={ if( issquare(1+8*n), return(1), return(0) ) ; } A000217(n)={ return(n*(n+1)/2) ; } isA087598(n)={ local(nredu) ; nredu=n ; while( nredu>10, if( isA000217(nredu), nredu=dd(nredu), return(0) ) ; ) ; if( isA000217(nredu), return(1), return(0) ) ; } { for(k=4, 1000000, if(isA087598(A000217(k)), print1(A000217(k), ", ") ; ) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
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CROSSREFS
| Cf. A087597, A087599, A087600.
Sequence in context: A164712 A181450 A087597 * A165403 A097386 A108685
Adjacent sequences: A087595 A087596 A087597 * A087599 A087600 A087601
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KEYWORD
| base,more,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 18 2003
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
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