A262577 Concatenation of the numbers from 1 to n but omitting 7.

1, 12, 123, 1234, 12345, 123456, 1234568, 12345689, 1234568910, 123456891011, 12345689101112, 1234568910111213, 123456891011121314, 12345689101112131415, 1234568910111213141516, 123456891011121314151617, 12345689101112131415161718, 1234568910111213141516171819, 123456891011121314151617181920

Offset: 1

Author

N. J. A. Sloane, Sep 25 2015

Keywords

• nonn
• base

Comments

There are only three primes among the first 98 terms: 123456891011,

12345689101112131415161718192021222324252627282930313233343536373839, and

12345689101112131415161718192021222324252627282930313233343536373839\

40414243444546474849505152535455565758596061626364566676869707172737\

475767778798081828384858687.

Does the sequence contain any other primes?

Yes, PARI reports the next (probable) prime after appending 13097; it has 54655 digits. - Bill McEachen, Oct 13 2015

Crossrefs

Cf. A007908, A262299, A262571-A262582.

See A262300 for more about this problem.

Programs

Mathematica

DeleteDuplicates@ Table[If[n >= 7, FromDigits@ Delete[Flatten[IntegerDigits /@ Range[n + 1]], 7], FromDigits@ Flatten[IntegerDigits /@ Range@ n]], {n, 19}] (* Michael De Vlieger, Oct 13 2015 *)

Formula

(a(n) - a(n-1)) mod 2 = 0 only for n=7. - Altug Alkan, Oct 15 2015