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A240570
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Prime numbers n such that replacing each digit in the decimal expansion of n with the sum of the other digits produces a prime.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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983 is in the sequence because 983 becomes 111217 which is also prime, where 11=8+3, 12=9+3 and 17=9+8.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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