A236036 a(n) is the smallest (2n+1)-digit prime number whose central digit equals the sum of its other digits.

10513, 1005013, 100040201, 10000400021, 1000004000111, 100000040002001, 10000000400000111, 1000000004000100011, 100000000040000000021, 10000000000400010000011, 1000000000004000000000111, 100000000000040000010000101, 10000000000000400000000011001

Offset

2,1

Comments

Sequence starts at n=2, since no such 3-digit prime exists.

Links

Giovanni Resta, Table of n, a(n) for n = 2..100

Example

a(3) = 1005013 because the central digit 5 equals the sum of the other digits 1+0+0+0+1+3.

Maple

with(numtheory):for n from 2 to 10 do:m:=2*n-2:ii:=1:ii:=0:for k from 10^m to 10^(m+1)-1 while(ii=0)do:x:=convert(k, base, 10):n1:=nops(x):s:=sum('x[j]', 'j'=1..n1):s1:=s-x[n]:if x[n]=s1 and type(k, prime)=true then ii:=1: printf ( "%d %d \n", n, k):else fi:od:od:

Mathematica

a[n_] := Catch@Block[{p}, Do[p = Select[ Union[ FromDigits /@ Flatten[ Permutations /@ (IntegerPartitions[d + n - 1, {n}, Range@d] - 1), 1]] + d*10^n + 10^(2*n), PrimeQ, 1]; If[p != {}, Throw@p[[1]]], {d, {4, 5}}]]; a /@ Range[2, 14] (* Giovanni Resta, Jan 20 2014 *)

Prog

(PARI) isspecial(p, n) = {d = digits(p); s = sumdigits(p); d[n+1] == (s - d[n+1]); }
a(n) = {forprime (p = 10^(2*n), 10^(2*n+1), if (isspecial(p, n), return (p)); ); return (0); } \\ Michel Marcus, Jan 19 2014

Crossrefs

Cf. A000040, A235119.

Sequence in context: A348758 A214192 A235119 * A216489 A120500 A371623

Adjacent sequences: A236033 A236034 A236035 * A236037 A236038 A236039

Keyword

nonn,base

Author

Michel Lagneau, Jan 18 2014

Extensions

a(9)-a(14) from Giovanni Resta, Jan 20 2014

Name simplified by Jon E. Schoenfield, Sep 09 2017

Status

approved