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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
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, ...
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 08 2014
STATUS
approved