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A193573
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Least happy number with next happy number of distance n.
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1
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31, 68, 7, 19, 23, 1, 219, 293, 70, 193, 208, 32, 748, 1233, 1457, 973, 263, 338, 49, 109, 763, 5606, 239, 1487, 8884, 1933, 1636, 139, 1607, 3932, 409, 18280, 17966, 4366, 4960, 16181, 33464, 3564, 18899, 496, 4995, 566, 144164, 3392, 5066, 388292, 194962, 178085
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OFFSET
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1,1
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COMMENTS
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The next term, a(43), equals 144164. [From Harvey P. Dale, Aug 27 2011]
a(88) = 469999871, a(92) = 488849933, a(96) = 1289999763, a(95) = 1688999664, a(104) = 3999991962, a(116) = 5888999662. - Chai Wah Wu, Aug 03 2023
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LINKS
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EXAMPLE
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a(1) = 31 since next happy number is 32 with distance 1.
a(2) = 68 since next happy number is 70 with distance 2.
a(3) = 7 since next happy number is 10 with distance 3.
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MATHEMATICA
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hapQ[n_]:=Last[NestWhileList[Total[IntegerDigits[#]^2]&, n, !MemberQ[{0, 1, 4, 16, 20, 37, 42, 58, 89, 145}, #]&]]==1; Transpose[With[ {hapnos= Partition[ Select[Range[34000], hapQ], 2, 1]}, Table[First[Select[ hapnos, Last[#]-First[#]==n&]], {n, 42}]]][[1]] (* Harvey P. Dale, Aug 27 2011 *)
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PROG
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(Python)
from itertools import count
a = 1
for k in count(2):
m = k
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:
if k-a==n:
return a
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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