A320571 a(0) = 1; thereafter a(n) is the smallest prime divisor of the number C(6n+1) formeded from the concatenation of 1,2,3,...,6n+1.

1, 127, 113, 13, 5, 29, 71, 7, 23, 5, 10386763, 397, 37907, 73, 5, 37, 13, 131, 7, 5, 278240783, 53, 8223519074965787731, 13, 5, 7, 11, 2381, 2671, 5, 31, 349, 7, 151, 5, 883, 13, 11, 19, 5, 521, 31, 79, 4861, 5, 17, 7, 17, 11, 5, 47, 2618101, 709, 7, 5, 219059, 17, 19, 31, 5, 7, 173, 13, 443, 5, 269534025881, 41, 7, 1229, 5, 11, 3899827, 8699, 61, 5, 13, 19

Offset

0,2

Comments

A075019(6n + k) for k = {2,3,4,5,6} is {2, 3, 2, 3, 2}.

No C(6n+1) has been found to be prime below C(344869).

Links

Table of n, a(n) for n=0..76.

Formula

a(n) = A075019(6n+1).

Example

For a(1), 1234567 = 127*9721, so a(1) = 127.
For a(10), C(61) = A007908(61) = 10386763 * 35280457769357 * 33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371.

Mathematica

f[n_] := Block[{p = 5, s = FromDigits[ Flatten[ IntegerDigits[ Range[ 6n + 1]]]]}, While[ Mod[s, p] > 0, p = NextPrime@ p]; p]; f[0] = 1; Array[ f, 77, 0]

Crossrefs

Cf. A007908, A075019.

Sequence in context: A340344 A180352 A217557 * A082456 A326717 A080540

Adjacent sequences: A320568 A320569 A320570 * A320572 A320573 A320574

Keyword

base,nonn

Author

Robert G. Wilson v, Oct 15 2018

Status

approved