A327820 Smallest prime with n holes in its decimal digits.

2, 19, 83, 89, 809, 1889, 4889, 46889, 48889, 468889, 688889, 3888889, 4888889, 28888889, 88884889, 288888889, 808888889, 4488888889, 8688888889, 48808888889, 48888888889, 288888888889, 888088888889, 1888888888889, 4888888888889, 48808888888889, 88848888888889

Offset

0,1

Comments

Smallest prime p such that A064692(p) = n. Also record-holders in A327462. - Felix Fröhlich, Sep 27 2019

The sequence is not monotonically increasing: a(32) > a(33). - Giovanni Resta, Sep 27 2019

Links

Giovanni Resta, Table of n, a(n) for n = 0..100

Mathematica

s[0] = {1, 2, 3, 5, 7}; s[1] = {0, 4, 6, 9}; s[2] = {8}; m[{sn_, t_}] := Union[Sort /@ Tuples[s[sn], {t}]]; f[nd_, nh_] := Block[{v, pa = Tally /@ IntegerPartitions[ nh, {nd}, {0, 1, 2}], bst = Infinity}, Do[v = Flatten /@ Tuples[m /@ p]; Do[z = Select[ FromDigits /@ Select[ Permutations[e], First[#] > 0 && OddQ[Last[#]] &], PrimeQ]; bst = Min[bst, {z}], {e, v}], {p, pa}]; bst]; a[0]=2; a[n_] := Block[{nd = Ceiling[(n + 1)/2], b}, While[! IntegerQ@ (b = f[nd, n]), nd++]; b]; a /@ Range[0, 30] (* Giovanni Resta, Sep 27 2019 *)

Prog

(PARI) count_holes(n) = my(d=digits(n), i=0); for(k=1, #d, if(d[k]==0 || d[k]==4 || d[k]==6 || d[k]==9, i++, if(d[k]==8, i+=2))); i
a(n) = forprime(p=1, , if(count_holes(p)==n, return(p))) \\ Felix Fröhlich, Sep 27 2019

Crossrefs

Cf. A064692, A249572, A250256, A327462.

Sequence in context: A057326 A129446 A240280 * A331898 A054570 A135436

Adjacent sequences: A327817 A327818 A327819 * A327821 A327822 A327823

Keyword

nonn,base

Author

Andrew Heathwaite, Sep 26 2019

Extensions

a(7) corrected and more terms added by Felix Fröhlich, Sep 27 2019

More terms from Giovanni Resta, Sep 27 2019

Status

approved