A320223 First occurrence of the n-th prime in A075019.

2, 3, 25, 43, 157, 19, 271, 229, 49, 31, 181, 91, 397, 481, 301, 127, 511, 439, 2701, 37, 79, 253, 793, 1531, 1237, 523, 1867, 637, 5293, 13, 7, 103, 3871, 3361, 4387, 199, 829, 2341, 2143, 367, 6511, 3967, 6391, 5617, 7711, 1273, 3217, 1621, 8767, 3157, 3013

Offset

1,1

Comments

Conjecture: All primes are present in A075019.

Records: 2, 3, 25, 43, 157, 271, 397, 481, 511, 2701, 5293, 6511, 7711, 8767, 11941, 12061, 25651, 30901, 30919, 47239, 64033, 145591, etc.

Links

Table of n, a(n) for n=1..51.

Example

a(1) = 2 since the first prime, 2, divides 12;
a(2) = 3 since the second prime, 3, divides 123;
a(3) = 25 since the third prime, 5, divides 12345678910111213141516171819202122232425; although 5 also divides 12345, so does 3 which is less than 5.

Mathematica

f[n_] := f[n] = Block[{p = Prime@ n, k = 1}, While[s = FromDigits@ Flatten[ IntegerDigits@# & /@ Range@ k]; Mod[s, p] > 0 || Union[Mod[s, Prime@ Range[n - 1]]][[1]] == 0, k += 2]; k]; f[1] = 2; Array[f, 51]

Crossrefs

Cf. A000040, A075019.

Sequence in context: A291262 A307922 A048674 * A296275 A295328 A281169

Adjacent sequences: A320220 A320221 A320222 * A320224 A320225 A320226

Keyword

nonn,base

Author

Robert G. Wilson v, Oct 07 2018

Status

approved