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

Author

Harvey P. Dale, Aug 02 2002

Keywords

• nonn
• base

Examples

			7480 is included because 7480, 7481 and 7482 are all happy numbers.
		

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

Programs

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 *)