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A052022 Smallest number m larger than prime(n) such that prime(n) = sum of digits of m and prime(n) = largest prime factor of m (or 0 if no such number exists). 7
12, 50, 70, 308, 364, 476, 1729, 4784, 9947, 8959, 38998, 588965, 179998, 1879859, 5988788, 38778989, 79693999, 287978998, 1489989599, 4595969989, 6888999949, 45999897788, 197999598599, 3999966997975, 6849998899886, 7885998969988, 35889999789995, 39969896999968 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Does there exist a solution for every prime p?

LINKS

Table of n, a(n) for n=2..29.

EXAMPLE

p=43 -> a(14)=179998 -> 1+7+9+9+9+8 = 43 and 179998 = 2*7*13*23*43. p=47 -> a(15)=1879859 -> 1+8+7+9+8+5+9 = 47 and 1879859 = 23*37*47*47.

MAPLE

A052022(n) = {

  local( p, m );

  p=prime(n) ;

  for(k=2, 1000000000,

    m=k*p;

    if( A007953(m) == p && A006530(m) == p,

        return(m) ;

    )

  ) ;

} /* R. J. Mathar, Mar 02 2012 */

MATHEMATICA

snm[n_]:=Module[{k=2, p=Prime[n], m}, m=k p; While[Total[ IntegerDigits[ m]]!=p||FactorInteger[m][[-1, 1]]!=p, k++; m=k p]; m]; Array[snm, 18, 2](* Harvey P. Dale, Feb 28 2012 *)

CROSSREFS

Cf. A052018, A052019, A052020, A052021, A007953, A005349, A028834.

Sequence in context: A041274 A029586 A081292 * A110907 A009937 A009932

Adjacent sequences:  A052019 A052020 A052021 * A052023 A052024 A052025

KEYWORD

nonn,base,nice

AUTHOR

Patrick De Geest, Nov 15 1999

EXTENSIONS

a(20)-a(29) from Donovan Johnson, May 09 2012

STATUS

approved

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Last modified November 18 21:51 EST 2017. Contains 294912 sequences.