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A084559 Smallest a(n) > n such that concatenation of numbers from n to a(n) is a prime or 0 if no such number exists. 6
3, 19, 7, 17, 7, 13, 9, 187 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Terms a(1) and a(10) (and many other terms) are currently unknown.
a(11) = 309, a(12) = 13.
a(1) > 344869 (see A007908). - Sean A. Irvine, Jun 17 2019
More terms: a(14..17) = (17, 19, 43, 39), a(20) = 23, a(23) = 41, a(25) = 49, a(26) = 147, a(28) = 73, a(33..39) = (103, 37, 603, 37, 43, 57, 43), a(42) = 43, a(44) = 51, a(49) = 241, a(50) = 51, a(n) > 1000 for 12 < n < 50 not mentioned here. - M. F. Hasler, Feb 22 2021
a(10) > 10010, a(18) = 3607, a(66) = 1003, a(275) = 1089. If n == 2 (mod 3), then a(n) == 3 or 5 (mod 6). If n == 0 or 1 (mod 3), then a(n) == 1 (mod 6) (see A341716). - Chai Wah Wu, Feb 22 2021
LINKS
Eric Weisstein's World of Mathematics, Consecutive Number Sequences.
Eric Weisstein's World of Mathematics, Smarandache Prime
EXAMPLE
a(4) = 7 because 4567 is a prime.
PROG
(PARI) A084559(n, N=n, T=10^logint(n, 10))=while(T*=10, for(m=n+1, n=T-1, ispseudoprime(N=N*T+m)&&return(m))) \\ M. F. Hasler, Feb 22 2021
CROSSREFS
Cf. also A341715, A341716, A341717 (similar but a(n) = n when n is prime).
Sequence in context: A258007 A293700 A114365 * A272815 A179767 A244605
KEYWORD
nonn,base,hard,more
AUTHOR
Zak Seidov, Jun 27 2003
EXTENSIONS
Edited by Max Alekseyev, Jan 28 2012
a(4) corrected by Daniel Suteu, Jun 16 2019
Escape clause added to definition by Chai Wah Wu, Feb 22 2021
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)