A231433 The digits of a(n) and a(n+1) taken together are the digits of a prime; least permutation of the nonnegative integers with this property.

0, 11, 2, 3, 1, 4, 7, 6, 10, 9, 5, 12, 8, 18, 13, 15, 14, 17, 20, 23, 21, 16, 19, 22, 30, 25, 27, 26, 29, 24, 31, 28, 33, 32, 35, 36, 34, 37, 39, 38, 41, 42, 43, 45, 47, 44, 51, 40, 49, 46, 57, 50, 53, 48, 59, 56, 63, 52, 61, 54, 67, 55, 69, 58, 70, 60, 71, 62, 72

Offset

0,2

Comments

The offset is zero to have a permutation.

Sequence A128280 is an "arithmetic" analog, where instead of concatenation of digits, the terms are added.

Sequences A228407 and A228410 are the variants where "prime" is replaced by "palindrome".

Links

Lars Blomberg, Table of n, a(n) for n = 0..9999

E. Angelini, Two make a prime, Nov 09 2013

Example

Start with a(0)=0. The least prime having this digit is 101, so a(1)=11. Since 0 cannot be used any more and 111 is not a prime, the least digit that can be added to get the digits of some prime (namely 211) is a(2)=2, then a(3)=3 yields 23, etc.
See also the link to Angelini's post.

Prog

(PARI)  {a=u=0; for(n=1, 99, u+=1<<a; print1(a", "); for(k=1, 9e9, bittest(u, k)&&next; d=Vec(Str(a, k)); for(p=0, (#d)!-1, isprime(eval(concat(t=vecextract(d, numtoperm(#d, p)))))&&t[1]>"0"&&(a=k)&&next(3))))}

Crossrefs

Sequence in context: A099268 A070277 A109864 * A240454 A375102 A377669

Adjacent sequences: A231430 A231431 A231432 * A231434 A231435 A231436

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Nov 09 2013

Status

approved