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A131839 Additive persistence of Sierpinski numbers of first kind. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 25 06:44 EST 2022. Contains 350565 sequences. (Running on oeis4.)