A272892 Taxi-cab numbers n such that n-1 and n+1 are both prime.

32832, 513000, 2101248, 8647128, 43570872, 46661832, 152275032, 166383000, 175959000, 351981000, 543449088, 610991208, 809557632, 970168752, 1710972648, 2250265752, 2262814272, 2560837032, 3222013032, 3308144112, 3582836712, 4505949000, 4543936488, 4674301632, 4868489178

Offset

1,1

Comments

Taxi-cab numbers that are in A014574.

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

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.

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..6385 a(n) for n = 1..88 from Charles R Greathouse IV

Example

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

Prog

(PARI) T=thueinit(x^3+1, 1);
isA001235(n)=my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1
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

Crossrefs

Cf. A001235, A014574.

Sequence in context: A168634 A045061 A183889 * A230524 A168666 A353019

Adjacent sequences: A272889 A272890 A272891 * A272893 A272894 A272895

Keyword

nonn

Author

Altug Alkan, May 09 2016

Extensions

a(7)-a(25) from Charles R Greathouse IV, May 09 2016

Status

approved