A331898 The smallest prime number with exactly n circular loops in its decimal representation.
2, 19, 83, 89, 809, 1889, 8089, 48889, 88883, 828889, 688889, 3888889, 8868889, 28888889, 88888883, 288888889, 808888889, 6886888889, 8688888889, 48888888889, 188688888889, 288888888889, 888088888889, 1888888888889, 8888988888889, 58888888888889, 188880888888889
Offset: 0
Examples
a(3) = 89 because 8 has two loops and 9 has one loop for a total of 3.
Links
- Giovanni Resta, Table of n, a(n) for n = 0..100
- Chris K. Caldwell and G. L. Honaker, Jr., Prime Curio for 19
Programs
-
Mathematica
Block[{s = Range[0, 15]}, Sort[#][[All, -1]] &@ Reap[Do[If[! FreeQ[s, #2], Sow[{#2, #1}]; s = DeleteCases[s, #2]] & @@ {#, Total[{0, 0, 0, 0, 0, 1, 0, 2, 1, 1} DigitCount[#]]} &@ Prime@ i, {i, 3*10^5}]][[-1, -1]]] (* Michael De Vlieger, Feb 08 2020 *) s[0]={1,2,3,4,5,7}; s[1]={0,6,9}; 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, Feb 09 2020 *) -
PARI
\\ here b(n) is A064532. b(n)={vecsum([if(d==8,2, d==0||d==6||d==9) | d<-digits(n)])} a(n)={forprime(p=1, oo, if(b(p)==n, return(p)))} \\ Andrew Howroyd, Jan 31 2020
Extensions
a(13)-a(16) from Andrew Howroyd, Jan 31 2020
a(17)-a(19) from Jinyuan Wang, Feb 08 2020
a(20)-a(26) from Giovanni Resta, Feb 09 2020
Comments