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A093807
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Palindromic numbers with property that sum of digits is prime and number of prime digits is prime.
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1
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212, 232, 272, 292, 313, 353, 373, 515, 535, 575, 595, 737, 757, 797, 12121, 12521, 12721, 13331, 13531, 13931, 15151, 15551, 15751, 17171, 17371, 17771, 20102, 20302, 20702, 20902, 21112, 21512, 21712, 22322, 22522, 23332, 23732, 24142
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OFFSET
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1,1
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COMMENTS
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a(1)=212, 212 is palindromic number, sum of digits 5 is prime, number of prime digits {2,2} 2 is prime, a(10)=575, 575 is palindromic number, sum of digits 17 is prime, number of prime digits {5,5,7} 3 is prime, a(15)=12121, 12121 is palindromic number, sum of digits 7 is prime, number of prime digits {2,2} 2 is prime, ...
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LINKS
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MAPLE
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# Return list of digits stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i, ans) ]; od; RETURN(anstren); end: # Return number of prime digits ts_stpf:=proc(n) local i, stpf, ans, ans1; ans:=stev_sez(n): ans1:=[ ]: stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i, ans))='true') then stpf:=stpf+1; ans1:=[ op(ans1), op(i, ans) ]: fi od; RETURN(stpf) end: # Return 0, if palindrome, otherwise return 1 ts_numpal:=proc(n) local ad; ad:=convert(n, base, 10): if (ListTools[Reverse](ad)=ad) then return 0; else return 1; fi end: # Return sum of digits ts_vsota_stevk:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do stpf:=stpf+op(i, ans); od; RETURN(stpf) end: ts_pras_vsota_pra_stevk_palind:=proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(ts_vsota_stevk(i)) = 'true' and isprime(ts_stpf(i))='true' and ts_numpal(i)=0) then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pras_vsota_pra_stevk_palind(100000);
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MATHEMATICA
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Cases[If[PalindromeQ@#, {#, {Count[IntegerDigits@#, _?PrimeQ], DigitSum@#}}, Nothing] & /@ Range@60000, {a_, {_?PrimeQ ..}} :>a] (* Hans Rudolf Widmer, Jul 26 2024 *)
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PROG
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(Python)
from sympy import isprime, nextprime
from itertools import count, islice, product
def pals(d): # all d-digit palindromes with odd middle digit, as strings
for p in product("0123456789", repeat=d//2):
if d//2 > 0 and p[0] == "0": continue
left = "".join(p); right = left[::-1]
for mid in [[""], "13579"][d%2]: yield left + mid + right
def agen(): # generator of terms
for d in count(3, 2):
yield from (int(p) for p in pals(d) if isprime(sum(1 for s in p if s in "2357")) and isprime(sum(map(int, p))))
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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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