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

0,1

Comments

The last digit of n cannot be 4, therefore a(n) must have at least n+1 digits. It is probable that none among [10^n/9]*40 + {1,3,7,9} is prime in which case a(n) must have n+2 digits. We conjecture that for all n >= 0, a(n) equals [10^(n+1)/9]*40 + b with 1 <= b <= 9 and one of the (first) digits 4 replaced by a 0, 1, 2 or 3. - M. F. Hasler, Feb 22 2016

Links

M. F. Hasler, Table of n, a(n) for n = 0..200

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}]

Prog

(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

Crossrefs

Cf. A065587, A037060, A034388, A036507-A036536.

Cf. A037053, A037055, A037057, A037059, A037063, A037065, A037067, A037069, A037071.

Sequence in context: A142160 A174615 A109125 * A065587 A264453 A112767

Adjacent sequences: A037058 A037059 A037060 * A037062 A037063 A037064

Keyword

nonn,base

Author

Patrick De Geest, Jan 04 1999

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

Status

approved