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%I #19 Aug 12 2021 10:50:44
%S 1878781,1879781,1968691,3589853,7819187,108484801,159181951,
%T 160696061,175090571,187090781,316686613,319393913,725585527,
%U 728888827,731898137,904080409,921191129,930494039,987191789,987484789,10456865401,10744944701
%N First of three consecutive palindromes all of which are prime.
%H Charles R Greathouse IV, <a href="/A032595/b032595.txt">Table of n, a(n) for n = 1..10000</a>
%H P. De Geest, <a href="http://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>
%e 2,3,5 are palindromes, and consecutive primes, but they are not consecutive palindromes.
%e 2,3,4 are consecutive palindromes, but they are not all primes.
%e The first time there are three consecutive palindromes which are all primes is 1878781, 1879781, 1880881. - _N. J. A. Sloane_, Aug 12 2021
%o (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
%o 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
%Y Cf. A002385, A032596, A032597.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, May 15 1998
%E New name from _Charles R Greathouse IV_, Aug 11 2021
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