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A088289
Triangular numbers in which the sum of the external digits equals the sum of the internal digits.
1
231, 253, 561, 990, 2211, 4095, 5050, 5151, 6903, 9180, 11325, 11628, 20301, 20503, 31626, 41041, 51040, 53301, 63546, 66066, 67528, 76245, 92665, 95703, 97020, 98346, 99235, 130305, 131328, 161028, 203203, 313236, 343206, 416328, 500500
OFFSET
1,1
COMMENTS
Includes A000217(2*10^k + 1) and A000217(2*10^k + 2) for k >= 1, A000217(10^k), A000217(10^k + 1), A000217(12*10^i + 9), A000217(12*10^i + 12) and A000217(4*10^(2*i) + 6*10^i + 3) for k >= 2, and A000217(4*10^k + 51), A00217(4*10^k + 63) and A000217(14*10^k + 14) for k >= 3. - Robert Israel, Oct 30 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..295 (first 203 terms from Harvey P. Dale)
EXAMPLE
4095 is a term: 4 + 5 = 9 = 0 + 9.
MAPLE
a:=proc(n) local nn: nn:=convert(n*(n+1)/2, base, 10): if sum(nn[j], j=2..nops(nn)-1)=nn[1]+nn[nops(nn)] then n*(n+1)/2 else fi end: seq(a(n), n=1..1300); # Emeric Deutsch, Aug 06 2005
MATHEMATICA
Do[d = IntegerDigits[n*(n+1)/2]; l = Length[d]; s = d[[1]] + d[[l]]; If[Plus @@ d == 2*s, Print[n*(n+1)/2]], {n, 1, 10^3}] (* Ryan Propper, Aug 06 2005 *)
edidQ[n_]:=Module[{idn=IntegerDigits[n]}, Total[idn[[1]]+idn[[-1]]]== Total[ Most[ Rest[idn]]]]; Select[Accumulate[Range[2000]], edidQ]//Quiet (* Harvey P. Dale, Nov 23 2022 *)
CROSSREFS
Intersection of A000217 and A101317.
Sequence in context: A031965 A316095 A345795 * A046009 A350367 A337231
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Sep 29 2003
EXTENSIONS
Corrected and extended by David Wasserman, Emeric Deutsch and Ryan Propper, Aug 06 2005
Offset changed by Andrew Howroyd, Sep 21 2024
STATUS
approved