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.

3, 19, 7, 17, 7, 13, 9, 187

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

a(10) > 50000. - Michael S. Branicky, Feb 25 2025

Links

Table of n, a(n) for n=2..9.

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. A007908, A030458, A030471, A052087, A052088, A052089.

Cf. also A341715, A341716, A341717 (similar but a(n) = n when n is prime).

Sequence in context: A258007 A293700 A114365 * A272815 A179767 A244605

Adjacent sequences: A084556 A084557 A084558 * A084560 A084561 A084562

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