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

Author

Zak Seidov, Jun 27 2003

Keywords

• nonn
• base
• hard
• more

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

Examples

			a(4) = 7 because 4567 is a prime.
		

Links

• Eric Weisstein's World of Mathematics, Consecutive Number Sequences.
• Eric Weisstein's World of Mathematics, Smarandache Prime

Crossrefs

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

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

Programs

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

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