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A072494
First of triples of consecutive happy numbers, i.e., the first of three consecutive integers each of which is a happy number (A007770).
4
1880, 4780, 4870, 7480, 7839, 7840, 8180, 8470, 8739, 8740, 8810, 10880, 11248, 11249, 11519, 12148, 12149, 13898, 15119, 18080, 18800, 21148, 21149, 23308, 25680, 25860, 26580, 26850, 28560, 28650, 31898, 32308, 33208, 33319, 40780, 40870, 44488, 44489
OFFSET
1,1
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 154 (Rev. ed. 1997).
LINKS
Eric Weisstein's World of Mathematics, Happy Number
EXAMPLE
7480 is included because 7480, 7481 and 7482 are all happy numbers.
MATHEMATICA
happyQ[n_] := Nest[Plus @@(IntegerDigits[ # ]^2\)&, n, 50] == 1); Transpose[Select[Partition[Select[Range[50000], happyQ], 3, 1], #[[3]] - #[[2]] == #[[2]] - #[[1]] == 1 &]][[1]]
f[n_] := Total[IntegerDigits[n]^2]; t = Select[Range[50000], NestWhile[f, #, UnsameQ, All] == 1 &]; t[[Select[Range[Length[t] - 2], t[[#]] == t[[# + 1]] - 1 == t[[# + 2]] - 2 &]]] (* T. D. Noe, Aug 23 2011 *)
SequencePosition[Table[If[FixedPoint[Total[IntegerDigits[#]^2]&, n, 100]==1, 1, 0], {n, 45000}], {1, 1, 1}][[All, 1]] (* Harvey P. Dale, Jun 19 2022 *)
CROSSREFS
Sequence in context: A320719 A358147 A235193 * A260137 A246478 A237103
KEYWORD
nonn,base
AUTHOR
Harvey P. Dale, Aug 02 2002
STATUS
approved