|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 154 (Rev. ed. 1997).
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|