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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Subsequence of A059168 (undulating primes).
Sequence in context: A056709 A243825 A345728 * A134809 A256186 A119680
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 04 2019
STATUS
approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)