A032595 First of three consecutive palindromes all of which are prime.

1878781, 1879781, 1968691, 3589853, 7819187, 108484801, 159181951, 160696061, 175090571, 187090781, 316686613, 319393913, 725585527, 728888827, 731898137, 904080409, 921191129, 930494039, 987191789, 987484789, 10456865401, 10744944701

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Examples

			2,3,5 are palindromes, and consecutive primes, but they are not consecutive palindromes.
2,3,4 are consecutive palindromes, but they are not all primes.
The first time there are three consecutive palindromes which are all primes is 1878781, 1879781, 1880881.  - _N. J. A. Sloane_, Aug 12 2021
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• P. De Geest, World!Of Palindromic Primes

Crossrefs

Cf. A002385, A032596, A032597.

Programs

PARI

nxt(n)=my(d=digits(n)); i=(#d+1)\2; while(i&&d[i]==9, d[i]=0; d[#d+1-i]=0; i--); if(i, d[i]++; d[#d+1-i]=d[i], d=vector(#d+1); d[1]=d[#d]=1); sum(i=1, #d, 10^(#d-i)*d[i]) \\ From David A. Corneth at A002113
list(lim)=my(v=List(),p=1,q=2,r=3); while(p<=lim\=1, if(isprime(r), if(isprime(q), if(isprime(p), listput(v,p)); p=q; q=r; r=nxt(r), q=nxt(p=r); r=nxt(q)), q=nxt(p=nxt(r)); r=nxt(q))); Vec(v) \\ Charles R Greathouse IV, Aug 11 2021

Extensions

New name from Charles R Greathouse IV, Aug 11 2021