A261965 Minimal appendage-sequence of primes with seed 1, base 10, and appendages of the form 0s(n); see Comments.

1, 101, 10103, 10103011, 10103011013, 1010301101309, 10103011013090003, 101030110130900030009, 10103011013090003000903, 1010301101309000300090303, 1010301101309000300090303009, 1010301101309000300090303009059, 1010301101309000300090303009059061

Offset

1,2

Comments

The minimal appendage-sequence of primes with seed s and base b is defined as follows:

a(1) = s

a(2) = least prime that begins with s0;

a(3) = least prime that begins with a(2)0;

a(n) = least prime that begins with a(n-1)0.

Links

Clark Kimberling, Table of n, a(n) for n = 1..300

Example

11 comes from a(3) = 10103 by appending 011 to a(3); the result is the least prime that begins with 10103. Triangular format:
1
101
10103
10103011
10103011013
1010301101309
10103011013090003
101030110130900030009

Mathematica

base = 10; s = {{1}}; Do[NestWhile[# + 1 &, 1, (nn = #; ! PrimeQ[FromDigits[tmp=IntegerDigits[FromDigits[Flatten[IntegerDigits[Join[Last[s], {0}, IntegerDigits[nn - Sum[base^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[base^n, {n, #}]) < 0) &] - 1}], base, l + 1]]]]]], base]]) &]; AppendTo[s, {FromDigits[tmp]}], {20}];
Flatten[s] (* Peter J. C. Moses, Sep 03 2015 *)

Crossrefs

Cf. A261966.

Sequence in context: A368417 A094028 A144564 * A255892 A065074 A113628

Adjacent sequences: A261962 A261963 A261964 * A261966 A261967 A261968

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 25 2015

Status

approved