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

1,1

Links

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

Prog

(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

Crossrefs

Cf. A000040, A002113.

Sequence in context: A060343 A080603 A179924 * A316603 A235914 A050716

Adjacent sequences: A274318 A274319 A274320 * A274322 A274323 A274324

Keyword

nonn,easy,base

Author

Giovanni Teofilatto, Jun 18 2016

Status

approved