%I #20 Jun 19 2022 15:53:51

%S 1880,4780,4870,7480,7839,7840,8180,8470,8739,8740,8810,10880,11248,

%T 11249,11519,12148,12149,13898,15119,18080,18800,21148,21149,23308,

%U 25680,25860,26580,26850,28560,28650,31898,32308,33208,33319,40780,40870,44488,44489

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

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 154 (Rev. ed. 1997).

%H Amiram Eldar, <a href="/A072494/b072494.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HappyNumber.html">Happy Number</a>

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

%t happyQ[n_] := Nest[Plus @@(IntegerDigits[ # ]^2\)&, n, 50] == 1); Transpose[Select[Partition[Select[Range[50000], happyQ], 3, 1], #[[3]] - #[[2]] == #[[2]] - #[[1]] == 1 &]][[1]]

%t 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 *)

%t 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 *)

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Aug 02 2002