A392990 Unhappy numbers that are sandwiched between two consecutive happy numbers.

69, 189, 191, 292, 330, 366, 564, 636, 654, 672, 762, 819, 900, 911, 922, 999, 1089, 1091, 1113, 1183, 1210, 1276, 1289, 1331, 1334, 1336, 1338, 1473, 1573, 1726, 1743, 1753, 1759, 1770, 1813, 1901, 2092, 2110, 2176, 2189, 2259, 2332, 2456, 2486, 2546, 2556

Offset

1,1

Comments

In other words, numbers k such that k - 1 and k + 1 are happy but k is not.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1310 from Xander Lee Luo)

Mathematica

happyQ[n_] := NestWhile[Total[IntegerDigits[#]^2] &, n, UnsameQ, All] == 1; seq[lim_] := Module[{h = Select[Range[lim], happyQ], ind}, ind = Position[Differences[h], 2] // Flatten; h[[ind]] + 1]; seq[2600] (* Amiram Eldar, Jan 30 2026 *)

Prog

(Python)
from itertools import count, islice
def ssd(n): return sum(int(d)**2 for d in str(n))
def is_happy(n):
    while n not in [1, 4]: n = ssd(n) # iterate until fixed point or in cycle
    return n==1
def agen(): # generator of terms
    h1, h2, h3 = True, False, False
    for k in count(2):
        if (h1, h2, h3) == (True, False, True): yield k
        h1, h2, h3 = h2, h3, is_happy(k+2)
print(list(islice(agen(), 46))) # Michael S. Branicky, Feb 04 2026

Crossrefs

Cf. A007770, A035502, A356412.

Sequence in context: A211688 A153672 A283053 * A249899 A009434 A228671

Adjacent sequences: A392987 A392988 A392989 * A392991 A392992 A392993

Keyword

nonn,base

Author

Xander Lee Luo, Jan 29 2026

Status

approved