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A274321 Primes equal to a concatenation of a prime and a nonzero palindromic number.

%I A274321 #37 Nov 15 2016 12:15:41
%S A274321 13,17,23,29,31,37,43,47,53,59,67,71,73,79,83,97,113,131,137,139,167,
%T A274321 173,179,191,193,197,199,211,223,227,229,233,239,241,271,277,283,293,
%U A274321 311,313,317,331,337,347,353,359,367,373,379,383,389,397,419,431,433,439
%N A274321 Primes equal to a concatenation of a prime and a nonzero palindromic number.
%H A274321 David A. Corneth, <a href="/A274321/b274321.txt">Table of n, a(n) for n = 1..4366</a>
%o A274321 (PARI) lista() = {my(l = List(), pal = vector(199,i,a2113(i)), pri = vector(primepi(10000)), t=0); forprime(i=2,10000,t++; pri[t]=i); for(i = 2, #pal, for(j=1,#pri, p = conc(pal[i], pri[j]); if(#digits(p) < 6, if(isprime(p), listput(l, p))); p = conc(pri[j], pal[i]); if(#digits(p) < 6, if(isprime(p), listput(l, p)))));listsort(l,1);l}a2113(n)={my(d, i, r); r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11)); n=n-10^(#digits(n\11)); d=digits(n); for(i=1, #d, r[i]=d[i]; r[#r+1-i]=d[i]); sum(i=1, #r, 10^(#r-i)*r[i])}
%o A274321 a2113(n)={my(d, i, r); r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11)); n=n-10^(#digits(n\11)); d=digits(n); for(i=1, #d, r[i]=d[i]; r[#r+1-i]=d[i]); sum(i=1, #r, 10^(#r-i)*r[i])}
%o A274321 conc(a, b) = {a * 10^(#digits(b)) + b} \\ _David A. Corneth_, Jun 18 2016
%o A274321 (PARI) ispal(n) = n && (eval(subst(Polrev(digits(n)), x, 10)) == n);
%o A274321 isconc(n) = {d = digits(n); for (k=1, #d, na = n\10^k; nb = n % 10^k; if ((n == eval(concat(Str(na), Str(nb)))) && ((isprime(na) && ispal(nb)) || (isprime(nb) && ispal(na))), return(1)););}
%o A274321 isok(n) = isprime(n) && isconc(n); \\ _Michel Marcus_, Jun 20 2016
%Y A274321 Cf. A000040, A002113.
%K A274321 nonn,easy,base
%O A274321 1,1
%A A274321 _Giovanni Teofilatto_, Jun 18 2016