A076712 Triangular numbers which are also happy numbers (cf. A007770).

1, 10, 28, 91, 190, 496, 820, 946, 1128, 1275, 2080, 2211, 2485, 3321, 4278, 8128, 8256, 8778, 9591, 9730, 11476, 12090, 12880, 13203, 13366, 13530, 15753, 16471, 17205, 17578, 20910, 21115, 21321, 22791, 24753, 25651, 27261, 29890, 30135, 31626, 33670, 35245

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Shyam Sunder Gupta Fascinating Triangular Numbers

Example

a(4)=91: 91 is a triangular number and also a happy number as 9^2+1^2=82, 8^2+2^2=68, 6^2+8^2=100 and 1^2+0^2+0^2=1. So 91 is triangular happy number.

Mathematica

Module[{nn=300, trnos, haps}, trnos=Accumulate[Range[nn]]; haps=Select[Range[ (nn(nn+1))/2], FixedPoint[ Total[IntegerDigits[#]^2]&, #, 10]==1&]; Intersection[ trnos, haps]] (* Harvey P. Dale, Aug 15 2014 *)

Prog

(Python)
from itertools import count, islice
def A076712_gen(): # generator of terms
    for n in count(1):
        m = t = n*(n+1)>>1
        while m not in {1, 37, 58, 89, 145, 42, 20, 4, 16}:
            m = sum((0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[ord(d)-48] for d in str(m))
        if m == 1:
            yield t
A076712_list = list(islice(A076712_gen(), 20)) # Chai Wah Wu, Aug 02 2023

Crossrefs

Cf. A000217, A007770.

Sequence in context: A333241 A251319 A126364 * A116973 A352180 A350990

Adjacent sequences: A076709 A076710 A076711 * A076713 A076714 A076715

Keyword

nonn,base

Author

Shyam Sunder Gupta, Oct 26 2002

Status

approved