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

13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 113, 131, 137, 139, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 271, 277, 283, 293, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 419, 431, 433, 439

Offset: 1

Author

Giovanni Teofilatto, Jun 18 2016

Keywords

• nonn
• easy
• base

Links

• David A. Corneth, Table of n, a(n) for n = 1..4366

Crossrefs

Cf. A000040, A002113.

Programs

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])}
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])}
conc(a, b) = {a * 10^(#digits(b)) + b} \\ David A. Corneth, Jun 18 2016

PARI

ispal(n) = n && (eval(subst(Polrev(digits(n)), x, 10)) == n);
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)););}
isok(n) = isprime(n) && isconc(n); \\ Michel Marcus, Jun 20 2016