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A131839
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Additive persistence of Sierpinski numbers of first kind.
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1
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0, 0, 2, 2, 2, 3, 2, 3, 3, 1, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 4, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 1, 3, 4, 3, 3, 4
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refs;
listen;
history;
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internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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Sierpinski number 257 --> 2+5+7 = 14 --> 1+4 = 5 thus persistence is 2.
The sixteenth Sierpinski number is 16^16 + 1 = 18446744073709551617 --> 1+8+4+4+6+7+4+4+0+7+3+7+0+9+5+5+1+6+1+7 = 89 --> 8+9 = 17 --> 1+7 = 8, thus a(16) = 3 because in three steps we obtain a number < 10. - Antti Karttunen, Dec 15 2017
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MAPLE
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f:= proc(n) local t, count;
t:= n^n+1;
count:= 0;
while t > 9 do
count:= count+1;
t:= convert(convert(t, base, 10), `+`);
od;
count
end proc:
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MATHEMATICA
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f[n_] := Length@ NestWhileList[Plus @@ IntegerDigits@# &, n^n + 1, UnsameQ@## &, All] - 2; Array[f, 105] (* Robert G. Wilson v, Dec 18 2017 *)
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PROG
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(PARI)
allocatemem(2^30);
A007953(n) = { my(s); while(n, s+=n%10; n\=10); s; };
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CROSSREFS
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KEYWORD
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easy,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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