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

Author

Altug Alkan, May 09 2016

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A001235, A014574.

Programs

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

Extensions

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