A272892 - OEIS

%I #19 May 14 2016 10:03:41

%S 32832,513000,2101248,8647128,43570872,46661832,152275032,166383000,

%T 175959000,351981000,543449088,610991208,809557632,970168752,

%U 1710972648,2250265752,2262814272,2560837032,3222013032,3308144112,3582836712,4505949000,4543936488,4674301632,4868489178

%N Taxi-cab numbers n such that n-1 and n+1 are both prime.

%C Taxi-cab numbers that are in A014574.

%C There are two versions of "taxicab numbers" that are A001235 and A011541. This sequence focuses on the version A001235.

%C First six terms are 2^6*3^3*19, 2^3*3^3*5^3*19, 2^12*3^3*19, 2^3*3^3*7^2*19*43, 2^3*3^6*31*241, 2^3*3^8*7*127.

%C This sequence contains many terms that are divisible by 6^3 = 216. But there are also terms that are not divisible by 6^3. For example, 166383*10^3 and 351981*10^3 are terms that are not divisible by 216.

%H Chai Wah Wu, <a href="/A272892/b272892.txt">Table of n, a(n) for n = 1..6385</a> a(n) for n = 1..88 from Charles R Greathouse IV

%e Taxi-cab number 32832 is a term because 32831 and 32833 are twin primes.

%o (PARI) T=thueinit(x^3+1,1);

%o isA001235(n)=my(v=thue(T,n)); sum(i=1,#v,v[i][1]>=0 && v[i][2]>=v[i][1])>1

%o p=2; forprime(q=3,1e9, if(q-p==2 && isA001235(p+1), print1(p+1", ")); p=q) \\ _Charles R Greathouse IV_, May 09 2016

%Y Cf. A001235, A014574.

%K nonn

%O 1,1

%A _Altug Alkan_, May 09 2016

%E a(7)-a(25) from _Charles R Greathouse IV_, May 09 2016