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Search: id:A101115
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| A101115 |
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Beginning with the n-th prime, the number of successive times a new prime can be formed by prepending the smallest nonzero digit. |
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+0
4
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| 0, 5, 0, 9, 5, 4, 8, 4, 5, 9, 4, 6, 2, 7, 6, 8, 9, 7, 6, 3, 14, 5, 5, 2, 4, 10, 1, 5, 7, 3, 4, 3, 5, 5, 0, 6, 5, 8, 5, 13, 4, 5, 4, 5, 3, 8, 4, 4, 5, 8, 3, 6, 1, 4, 4, 2, 5, 2, 2, 3, 4, 9, 8, 7, 4, 7, 3, 3, 5, 5, 7, 8, 4, 3, 3, 2, 1, 7, 0, 4, 3, 5, 3, 7, 9, 6, 6, 5, 6, 8
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It is possble the procedure described would generate some left-truncatable primes (A024785). Although zero digits cannot be added, it is possible the starting prime may contain zeros. Therefore the possible number of digit additions is not limited by the length of the largest known left-truncatable prime. Further, because the smallest digit that satisfies the requirement is used each time, it is possible that choosing a larger digit would allow more single digits to be added. Therefore although some of the set of left-truncatable primes may be generated by this practice, not all of them will.
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REFERENCES
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Angell, I. O. and Godwin, H. J. "On Truncatable Primes." Math. Comput. 31, 265-267, 1977.
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LINKS
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Index entries for sequences related to truncatable primes
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EXAMPLE
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a(2) is 5 because the second prime is 3, to which single nonzero digits can be prepended 5 times yielding a new prime each time (giving preference to the smallest digit that satisfies the requirement): 13, 113, 2113, 12113, 612113 (see A053583). There is no nonzero digit which can be prepended to 612113 to yield a new prime.
a(21) = 14 because the 21'st prime (73) can be prepended with single nonzero digits 14 times yielding a new prime each time: 73, 173, 6173, 66173, ..., 4818372912366173.
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CROSSREFS
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Cf. A053583, A024785, A000040, A101116, A101117, A101118.
Sequence in context: A141431 A132706 A019925 this_sequence A010481 A022898 A088307
Adjacent sequences: A101112 A101113 A101114 this_sequence A101116 A101117 A101118
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004
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