A072494 First of triples of consecutive happy numbers, i.e., the first of three consecutive integers each of which is a happy number (A007770).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A072491 A072492 A072493 * A072495 A072496 A072497

Keyword

nonn,base

Author

Harvey P. Dale, Aug 02 2002

Status

approved