A131839 Additive persistence of Sierpinski numbers of first kind.

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

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 2048 terms from Antti Karttunen)

Formula

a(n) = A031286(A014566(n)). - Antti Karttunen, Dec 15 2017

Example

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

Maple

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:
map(f, [$1..100]); # Robert Israel, Dec 18 2017

Mathematica

f[n_] := Length@ NestWhileList[Plus @@ IntegerDigits@# &, n^n + 1, UnsameQ@## &,     All] - 2; Array[f, 105] (* Robert G. Wilson v, Dec 18 2017 *)

Prog

(PARI)
allocatemem(2^30);
A007953(n) = { my(s); while(n, s+=n%10; n\=10); s; };
A031286(n) = { my(s); while(n>9, s++; n=A007953(n)); s; }; \\ This function after Charles R Greathouse IV, Sep 13 2012
A014566(n) = (1+(n^n));
A131839(n) = A031286(A014566(n)); \\ Antti Karttunen, Dec 15 2017

Crossrefs

Cf. A014566, A131836.

Sequence in context: A329046 A281856 A106696 * A143299 A239428 A257497

Adjacent sequences: A131836 A131837 A131838 * A131840 A131841 A131842

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 20 2007

Extensions

Erroneous terms (first at n=16) corrected by Antti Karttunen, Dec 15 2017

Status

approved