A309488 Primes whose decimal expansion is of the form d_1+0+d_2+0+d_3+0+...+0+d_k where d_i are digits with 1 <= d_i <= 9, k > 1 and + stands for concatenation.

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 10103, 10301, 10303, 10501, 10601, 10607, 10709, 10903, 10909, 20101, 20107, 20201, 20407, 20507, 20509, 20707, 20807, 20809, 20903, 30103, 30109, 30203, 30307, 30403, 30509, 30703, 30707, 30803, 30809

Offset

1,1

Comments

The terms of this sequence have necessarily an odd number >= 3 of digits.

There is only one term whose digits > 0 are all equal: 101.

The only cyclops primes (A134809) of this sequence are the first 15 terms from 101 to 907.

The first palindromes of this sequence are 101, 10301, 10501, 10601, 30103, 30203, 30403, 30703, 30803, ...

Intersection with A309101 = {503, 10103, 10303, 10903, ...}.

Links

Table of n, a(n) for n=1..44.

Example

103 is the smallest term with two distinct digits > 0.
10607 is the smallest term with three distinct digits > 0.

Mathematica

aQ[n_] := PrimeQ[n] && OddQ[(m = Length[(d = IntegerDigits[n])])] && Flatten@Position[d, _?(# == 0 &)] == Range[2, m, 2]; Select[Range[100, 31000], aQ] (* Amiram Eldar, Aug 04 2019 *)

Prog

(Magma) sol:=[]; m:=1; for p in PrimesInInterval(101, 50000) do  v:=Reverse(Intseq(p)); test:=0; for u in [1..#v-1] do if u mod 2 eq 0 and v[u] eq 0 and v[u+1] ne 0 then test:=test+1; end if; end for; if test eq (#v-1)/2 then sol[m]:=p; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 04 2019
(PARI) eva(n) = subst(Pol(n), x, 10)
f(n) = my(d=digits(n)); eva(vector(2*#d-1, k, if (k%2, d[1+k\2]))) \\ from Michel Marcus
terms(n) = my(i=0); for(k=10, oo, if(i>=n, break); if(vecmin(digits(k)) > 0, my(iz=f(k)); if(ispseudoprime(iz), print1(iz, ", "); i++)))
/* Print initial 40 terms as follows: */
terms(40) \\ Felix Fröhlich, Aug 08 2019

Crossrefs

Cf. A000040, A002385, A134809, A309101.

Subsequence of A059168 (undulating primes).

Sequence in context: A056709 A243825 A345728 * A134809 A256186 A119680

Adjacent sequences: A309485 A309486 A309487 * A309489 A309490 A309491

Keyword

nonn,base

Author

Bernard Schott, Aug 04 2019

Status

approved