A138360 Quintuples of 5 consecutive strictly non-palindromic primes.

3253177, 3253219, 3253223, 3253231, 3253241, 20189111, 20189119, 20189123, 20189137, 20189167, 22122937, 22122979, 22122983, 22123021, 22123043, 61309069, 61309081, 61309091, 61309093, 61309097, 89073521, 89073533, 89073583, 89073599, 89073613

Offset: 1

Author

Karl Hovekamp, Mar 16 2008

Keywords

• base
• hard
• nonn
• tabf

Comments

The quintuples T(n,1), T(n,2), .. T(n,5), n>=1, in this array are 5 consecutive primes (consecutive in A000040) which are also members of A016038.

Notice that all strictly non-palindromic numbers >6 are prime! (See A016038.) Quintuples of these strictly non-palindromic primes, without any normal prime in between, are listed here.

Up to 1 billion there are only 5 quintuples of strictly non-palindromic primes. May be that there are no more quintuples of this kind. Up to 1 billion there are no n-tuples of strictly non-palindromic primes with n>5.

Examples

			Primes:
...
3253153 palindromic in bases 203, 356, 495, 1316, 1442, 1504 and 1648
3253177 strictly non-palindromic
3253219 strictly non-palindromic
3253223 strictly non-palindromic
3253231 strictly non-palindromic
3253241 strictly non-palindromic
3253253 palindromic in bases 653, 768, 910 and 1001
...
So {3253177, 3253219, 3253223, 3253231, 3253241} is the first quintuple of the strictly non-palindromic primes.
		

References

• Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

Links

• K. Hovekamp, Palindromic numbers in different bases.
• K. Hovekamp, Strictly non-palindromic prime 5-tuple, quadruple and triple up to 1 billion
• Wikipedia, Strictly non-palindromic numbers.

Crossrefs

Cf. A138358 (triples), A138359 (4-tuples), A138329, A016038, A047811, A016038.

Extensions

More terms from Mauro Fiorentini, Jan 03 2016