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A066817 Conjectured values of first prime in the sequence of "reincarnations" f(m),f(f(m)),.... of m under f(m) = decimal encoding of the prime factorization of m (A067599), where m = n-th composite number, if this prime exists; = 0 otherwise. 1
0, 2131, 23, 3224591, 0, 0, 0, 0, 0, 0, 2251, 0, 0, 0, 3224591, 314313643123658229739531, 0, 0, 46747167851021731, 3224591, 3141114911731, 5171, 0, 21191, 3311531, 2351, 0, 22111, 3251, 32831437931, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

The terms with 0 value listed above are conjectural. There are no primes < 10^30.

LINKS

Table of n, a(n) for n=2..34.

MATHEMATICA

(*f returns an array encoding the prime factorization of n*) f[ n_] := Module[ {a, l, i, t = {} }, a = FactorInteger[ n]; l = Length[ a]; For[ i = 1, i <= l, i++, t = Append[ t, a[ [ i]][ [ 1]]]; t = Append[ t, a[ [ i]][ [ 2]]]]; t];

(*g returns the concatenation of the elements of its input array*) g[ x_] := Module[ {r = "", m = Length[ x], l}, For[ l = 1, l <= m, l++, r = StringJoin[ r, ToString[ x[ [ l]]]]]; r]; (*h returns an array of the digits of its input int string*) h[ n_] := IntegerDigits[ ToExpression[ n]]

(*j returns the number formed from the digits in its input array*) j[ x_] := Module[ {r = 0, m = Length[ x], t = x, l}, For[ l = 1, l <= m, l++, r = 10*r + t[ [ 1]]; t = Rest[ t]]; r]; (*k composes the previous functions*) k[ n_] := j[ h[ g[ f[ n]]]] s[ n_] := Module[ {a=n, r=0}, While[ !PrimeQ[ a] && a<10^30, a=k[ a]]; If[ PrimeQ[ a], r=a]; r]; Table[ s[ i], {i, 2, 50}]

CROSSREFS

Cf. A067599, A067600.

Sequence in context: A278797 A251134 A210271 * A110024 A260068 A237070

Adjacent sequences:  A066814 A066815 A066816 * A066818 A066819 A066820

KEYWORD

base,nonn

AUTHOR

Joseph L. Pe, Feb 01 2002

STATUS

approved

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Last modified December 7 03:45 EST 2016. Contains 278841 sequences.