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A112750 Smallest prime of the form 7 followed by j copies of the digit k, where j runs through those positive values for which such a prime exists. 0
71, 733, 7333, 79999, 733333, 71111111, 799999999, 79999999999, 79999999999999999999999999, 79999999999999999999999999999999999999999999999999, 733333333333333333333333333333333333333333333333333333, 71111111111111111111111111111111111111111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For all j > 0, k must be 1, 3, or 9, since a number with --
-- digits 7kk...kk where k is even will be a proper multiple of 2;
-- digits 755...55 will be a proper multiple of 5; and
-- digits 777...77 will be a proper multiple of 7.
LINKS
EXAMPLE
7333 is a term because it is prime and is 7 followed by three copies of 3, and the numbers 7000, 7111, and 7222 are all nonprime.
From Jon E. Schoenfield, Feb 23 2021: (Start)
Terms begin as follows:
n j k a(n)
-- -- - --------------------------------------------------------
1 1 1 71
2 2 3 733
3 3 3 7333
4 4 9 79999
5 5 3 733333
- 6 - (7111111, 7333333, 7999999 are composite)
6 7 1 71111111
7 8 9 799999999
- 9 - (7111111111, 7333333333, 7999999999 are composite)
8 10 9 79999999999
- 11 - (711111111111, 733333333333, 799999999999 are composite)
- 12 - (all composite)
- 13 - (all composite)
...
9 25 9 79999999999999999999999999
...
10 49 9 79999999999999999999999999999999999999999999999999
...
11 53 3 733333333333333333333333333333333333333333333333333333
12 55 1 71111111111111111111111111111111111111111111111111111111
(End)
MATHEMATICA
SelectFirst[#, PrimeQ]&/@Table[FromDigits[PadRight[{7}, n, p]], {n, 2, 60}, {p, {1, 3, 9}}]/.Missing["NotFound"]->Nothing (* Harvey P. Dale, Apr 19 2021 *)
CROSSREFS
Subset of A090155.
Sequence in context: A180327 A201039 A142674 * A351896 A089706 A220623
KEYWORD
base,nonn,less
AUTHOR
Amarnath Murthy, Jan 02 2006
EXTENSIONS
More terms added by Harvey P. Dale, Jan 24 2010
Name corrected (using a suggestion from Felix Fröhlich) and Example edited by Jon E. Schoenfield, May 28 2019
Terms corrected by Jon E. Schoenfield, Feb 23 2021
STATUS
approved

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Last modified March 4 02:53 EST 2024. Contains 370522 sequences. (Running on oeis4.)