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A340843 Emirps p such that p+(sum of digits of p) and reverse(p)+(sum of digits of p) are emirps. 2
1933, 3391, 32687, 78623, 104087, 109891, 112103, 120283, 123127, 135469, 136217, 161983, 162209, 162391, 163819, 179779, 193261, 198613, 198901, 301211, 316819, 316891, 382021, 389161, 712631, 721321, 726487, 738349, 780401, 784627, 902261, 918361, 918613, 943837, 964531, 977971, 1002247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

EXAMPLE

a(3) = 32687 is an emirp because 32687 and 78623 are distinct primes. The sum of digits of 32687 is 26. 32687+26 = 32713 and 78623+26 = 78649 are emirps because 32713 and 31723 are distinct primes, as are 78649 and 94687.

MAPLE

revdigs:= proc(n) local L, i;

  L:= convert(n, base, 10);

  add(10^(i-1)*L[-i], i=1..nops(L))

end proc:

filter:= proc(n) local r, t, n2, n3;

if not isprime(n) then return false fi;

r:= revdigs(n);

if r = n or not isprime(r) then return false fi;

t:= convert(convert(n, base, 10), `+`);

for n2 in [n+t, r+t] do

  if not isprime(n2) then return false fi;

  r:= revdigs(n2);

  if r = n2 or not isprime(r) then return false fi;

od;

true

end proc:

select(filter, [seq(i, i=13..10^6, 2)]);

PROG

(Python)

from sympy import isprime

def sd(n): return sum(map(int, str(n)))

def emirp(n):

  if not isprime(n): return False

  revn = int(str(n)[::-1])

  if n == revn: return False

  return isprime(revn)

def ok(n):

  if not emirp(n): return False

  if not emirp(n + sd(n)): return False

  revn = int(str(n)[::-1])

  return emirp(revn + sd(revn))

def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]

print(aupto(920000)) # Michael S. Branicky, Jan 24 2021

CROSSREFS

Cf. A006567. Contained in A340842.

Sequence in context: A227491 A277943 A251945 * A270265 A237010 A256765

Adjacent sequences:  A340840 A340841 A340842 * A340844 A340845 A340846

KEYWORD

nonn,base

AUTHOR

J. M. Bergot and Robert Israel, Jan 23 2021

STATUS

approved

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Last modified January 27 18:40 EST 2022. Contains 350611 sequences. (Running on oeis4.)