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.

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

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: A359137 A266675 A185104 * A354524 A162237 A325870

Adjacent sequences: A240567 A240568 A240569 * A240571 A240572 A240573

Keyword

nonn,base

Author

Michel Lagneau, Apr 08 2014

Status

approved