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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 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.)