A037061 Smallest prime containing exactly n 4's.
2, 41, 443, 4441, 44449, 444443, 24444443, 424444441, 444444443, 4444444447, 44444444441, 444444444443, 14444444444449, 440444444444441, 2444444444444447, 44044444444444441, 424444444444444447, 4344444444444444449, 42444444444444444443, 44444444444444444447
Offset: 0
Links
- M. F. Hasler, Table of n, a(n) for n = 0..200
Crossrefs
Programs
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Mathematica
f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[b, {i, 1, n}], {x}]], c = Complement[Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[r ? Infinity, r, p = Permutations[ Join[ Table[ b, {i, 1, n}], {x, y}]]; q = {}; Do[q = Append[q, Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]]]; Table[ f[n, 4], {n, 1, 18}] -
PARI
A037061(n)={my(p, t=10^(n+1)\9*40); forvec(v=[[-1, n], [-4, -1]], nextprime(p=t+10^(n-v[1])*v[2])-p<10 && return(nextprime(p)))} \\ M. F. Hasler, Feb 22 2016
Formula
a(n) = prime(A037060(n)). - Amiram Eldar, Jul 21 2025
Extensions
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
More terms and a(0) = 2 from M. F. Hasler, Feb 22 2016
Comments