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A114025
Least prime such that the n-th partial concatenation is a multiple of the n-th prime.
4
2, 7, 5, 17, 71, 23, 2, 53, 151, 191, 181, 61, 47, 61, 163, 373, 23, 29, 179, 167, 353, 691, 37, 7, 79, 43, 7, 73, 683, 757, 1259, 433, 113, 1523, 643, 19, 73, 383, 1907, 89, 2423, 457, 223, 2713, 71, 3253, 191, 17, 1069, 353, 1481, 1433, 787, 1009, 1753, 557, 3001
OFFSET
1,1
COMMENTS
In the first 750 terms, the primes 3,11,41,59,83,97,101,109,131,149,157,173,193,197,211,227, ..., have not appeared. - Robert G. Wilson v, Nov 19 2005
First appearances of some of those: 3 = a(2945), 41 = a(752), 101 = a(3436), 109 = a(2922), 131 = a(6858), 173 = a(5807), 197 = a(918). - Robert Israel, Dec 22 2025
LINKS
EXAMPLE
2 divides 2, 3 divides 27, 5 divides 275.
MAPLE
tcat:= proc(a, b) 10^(1+ilog10(b))*a+b end proc:
R:= 2: x:= 2:
for i from 2 to 100 do
p:= 2: q:= ithprime(i);
do
if tcat(x, p) mod q = 0 then break fi;
p:= nextprime(p);
od;
R:= R, p; x:= tcat(x, p);
od:
R; # Robert Israel, Dec 22 2025
MATHEMATICA
a[n_] := a[n] = Block[{q = Flatten[IntegerDigits /@ Table[a[i], {i, n - 1}]], p = Prime[n], k = 1}, While[Mod[FromDigits@Join[q, IntegerDigits@Prime@k], p] != 0, k++ ]; Prime[k]]; Array[a, 57] (* Robert G. Wilson v, Nov 19 2005 *)
CROSSREFS
See A133566 for another version.
Sequence in context: A343314 A233248 A376976 * A135566 A100759 A205448
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Nov 13 2005
EXTENSIONS
More terms from Robert G. Wilson v, Nov 19 2005
Definition corrected by David Wasserman, Mar 04 2008
STATUS
approved