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A240570 Prime numbers n such that replacing each digit in the decimal expansion of n with the sum of the other digits produces a prime. 0
11, 13, 17, 31, 37, 71, 73, 79, 97, 127, 163, 181, 211, 257, 271, 277, 293, 307, 349, 367, 431, 433, 457, 491, 521, 523, 541, 563, 587, 631, 659, 743, 839, 983, 10069, 10151, 10337, 10429, 10559, 10889, 10973, 11059, 11251, 11329, 11411, 11437, 11471, 11617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let d(1)d(2)...d(q) denote the decimal expansion of a prime number. Replace each digit d(i) in decimal expansion of n with Sum_{j=1..q, j<>i} d(j) such that the result is a prime number.

The corresponding primes are 11, 31, 71, 13, 73, 17, 37, 97, 79, 983, 947, 929, 233, 1297, 839, 1499, ...

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

983 is in the sequence because 983 becomes 111217 which is also prime, where 11=8+3, 12=9+3 and 17=9+8.

MAPLE

with(numtheory):T:=array(1..10):

   for n from 1 to 1000 do:

     p:=ithprime(n):k:=0:s:=0:j:=0:

     x:=convert(p, base, 10):n1:=nops(x):

     s1:=sum('x[i]', 'i'=1..n1):

       for m from n1 by -1 to 1 do:

       k:=k+1:T[k]:=s1-x[m]:

       od:

       n2:=sum('length(T[j])', 'j'=1..n1):s2:=0:

         for u from 1 to n1 do:

         s2:=s2+ T[u]*10^(n2-length(T[u])):n2:=n2-length(T[u]):

         od:

            if type(s2, prime)=true

            then

            printf(`%d, `, p):

            else

            fi:

     od:

CROSSREFS

Sequence in context: A111337 A266675 A185104 * A162237 A325870 A090236

Adjacent sequences:  A240567 A240568 A240569 * A240571 A240572 A240573

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 08 2014

STATUS

approved

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Last modified June 27 12:48 EDT 2022. Contains 354896 sequences. (Running on oeis4.)