A056527 -id:A056527 - cp's OEIS frontend

A031177 Unhappy numbers: numbers having period-8 2-digitized sequences.

2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83

Offset: 1

Eric W. Weisstein

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Digitaddition
Eric Weisstein's World of Mathematics, Unhappy Number

Complement of happy numbers A007770. Cf. A056527.

Cf. A003132, A103369.

a031177 n = a031177_list !! (n-1)
a031177_list = filter ((/= 1) . a103369) [1..]
-- Reinhard Zumkeller, Aug 24 2011

from itertools import count, islice
def A031177_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        m = n
        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 n
A031177_list = list(islice(A031177_gen(),20)) # Chai Wah Wu, Aug 02 2023

A056528 Sum of digits of square of sum of digits of square.

Original entry on oeis.org

1, 7, 9, 13, 13, 9, 16, 1, 9, 1, 7, 9, 13, 13, 9, 16, 10, 9, 1, 7, 9, 13, 13, 9, 16, 10, 9, 10, 16, 9, 13, 13, 9, 16, 1, 9, 10, 16, 9, 13, 13, 9, 16, 10, 9, 1, 16, 9, 13, 13, 9, 16, 10, 9, 1, 16, 9, 13, 13, 9, 16, 10, 18, 10, 16, 9, 13, 13, 9, 16, 1, 9, 10, 16, 9, 13, 13, 9, 16, 1, 9

Offset: 1

Henry Bottomley, Jun 19 2000

			a(2)=7 because sum of digits of square of 2 is 4 and sum of digits of square of 4 is 1+6=7

Cf. A004159 for sum of digits of square, A056020 where iteration settles to 1, A056020 where iteration settles to 9, A056527 where iteration settles to 13 and 16. See also A056529.

Array[Total[IntegerDigits[(Total[IntegerDigits[#^2]])^2]]&,90] (* Harvey P. Dale, Jan 17 2012 *)
Table[Nest[Total[IntegerDigits[#^2]]&,n,2],{n,90}] (* Harvey P. Dale, Mar 07 2018 *)

a(n)=A004159(A004159(n))

A056529 Number of iterations of sum of digits of square to reach 1, 9, 13 or 16.

Original entry on oeis.org

0, 3, 1, 2, 2, 1, 1, 2, 0, 1, 3, 1, 0, 1, 1, 0, 3, 1, 2, 3, 1, 1, 1, 2, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 2, 2, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 3, 1, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 1, 2, 2, 3, 2, 1, 3, 1, 1, 1, 1

Offset: 1

Henry Bottomley, Jun 19 2000

			a(2)=3 because successive iterations give 2 -> 4 -> 7 -> 13 -> 16 -> 13 etc.

Cf. A004159 for sum of digits of square, A056528 for two iterations, A056020 where iteration settles to 1, A056020 where iteration settles to 9, A056527 where iteration settles to 13 and 16.

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A031177 Unhappy numbers: numbers having period-8 2-digitized sequences.

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A056528 Sum of digits of square of sum of digits of square.

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A056529 Number of iterations of sum of digits of square to reach 1, 9, 13 or 16.

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