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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 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

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