A235119 Prime numbers whose central digit equals the sum of the other digits.

10513, 10531, 10733, 10861, 11411, 11503, 11833, 12401, 12511, 12713, 12823, 12841, 13721, 13831, 14821, 20411, 20521, 21401, 21713, 21841, 22501, 22721, 25801, 30713, 30841, 31721, 32803, 33811, 40813, 42701, 43801, 50821, 60811, 1005013, 1007231, 1008043

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..150

Example

10513 is in the sequence because the central digit 5 equals the sum of the other digits 1+0+1+3.

Maple

with(numtheory):for n from 2 to 4 do:m:=2*n-2:for k from 10^m to 10^(m+1)-1 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 printf(`%d, `, k):else fi:od:od:

Mathematica

cdsodQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=(Length[idn]+1)/2; OddQ[ IntegerLength[ n]]&&Total[Drop[idn, {len}]]==idn[[len]]]; Select[ Prime[ Range[ 80000]], cdsodQ] (* Harvey P. Dale, Nov 11 2017 *)

Crossrefs

Cf. A000040.

Sequence in context: A206322 A348758 A214192 * A236036 A216489 A120500

Adjacent sequences: A235116 A235117 A235118 * A235120 A235121 A235122

Keyword

nonn,base

Author

Michel Lagneau, Jan 18 2014

Extensions

Name simplified by Jon E. Schoenfield, Sep 09 2017

Status

approved