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A052035
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Palindromic primes whose sum of squared digits is also prime.
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3
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11, 101, 131, 191, 313, 353, 373, 797, 919, 10301, 11311, 12721, 13331, 13931, 14341, 14741, 16361, 17971, 18181, 19391, 30103, 30703, 33533, 71317, 71917, 74747, 75557, 76367, 77977, 79397, 90709, 93139, 93739, 95959, 96769, 97379
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OFFSET
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1,1
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COMMENTS
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Except for 11, all terms have an odd number of digits.
Except for terms of the form 10^k+1, k >= 2, the middle digit is always odd; the unique known term of the form 10^k+1 for 2 <= k <= 100000 is 101 (see comment in A000533). (End)
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REFERENCES
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Charles W. Trigg, Journal of Recreational Mathematics, Vol. 20(2), 1988.
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LINKS
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Mike Mudge, Morph code, Hands On Numbers Count, Personal Computer World, May 1997, p. 290.
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EXAMPLE
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373 -> 3^2 + 7^2 + 3^2 = 67, which is prime.
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MATHEMATICA
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Select[Prime@ Range[2, 10^4], And[PalindromeQ@ #, PrimeQ@ Total[IntegerDigits[#]^2]] &] (* Michael De Vlieger, Oct 20 2021 *)
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PROG
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(PARI) isok(p) = my(d=digits(p)); isprime(p) && (d==Vecrev(d)) && isprime(sum(k=1, #d, d[k]^2)); \\ Michel Marcus, Oct 17 2021
(Python)
from sympy import isprime
def ok(n):
s = str(n)
return s==s[::-1] and isprime(n) and isprime(sum(int(d)**2 for d in s))
(Python) # second version for going to large terms
from sympy import isprime
from itertools import product
def ok(pal):
return isprime(pal) and isprime(sum(int(d)**2 for d in str(pal)))
def agentod(maxdigs):
yield 11
for d in range(3, maxdigs+1, 2):
pal = 10**(d-1) + 1
if ok(pal): yield pal
for first in "1379":
for left in product("0123456789", repeat=(d-3)//2):
left = "".join(left)
for mid in "13579":
pal = int(first + left + mid + left[::-1] + first)
if ok(pal): yield pal
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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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