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

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

P. De Geest, World!Of Palindromic Primes

Example

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

Prog

(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

Crossrefs

Cf. A002385, A032596, A032597.

Sequence in context: A145276 A251008 A064820 * A230806 A032596 A032597

Adjacent sequences: A032592 A032593 A032594 * A032596 A032597 A032598

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

New name from Charles R Greathouse IV, Aug 11 2021

Status

approved