A191221 Numbers k such that k plus the sum of the digits of k is prime, and R(k) plus the sum of the digits of k is prime, where R(k) = A004086(k).

1, 10, 11, 19, 35, 37, 53, 59, 73, 91, 95, 100, 101, 143, 181, 218, 232, 250, 272, 296, 298, 323, 341, 343, 365, 383, 385, 418, 436, 454, 490, 509, 527, 547, 563, 583, 610, 634, 650, 656, 670, 692, 725, 727, 745, 749, 767, 787, 812, 814, 838, 850, 892, 905, 947, 949, 1009

Offset

1,2

Comments

Numbers ending with zero(s) when reversed have fewer digits.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Example

143 and 341 belong to the sequence since 143 + (1+4+3) = 151 is prime and 341 + (3+4+1) = 349 is also a prime.

Maple

read(transforms): isA191221 := proc(n) local r: r:=digrev(n): return (isprime(n+digsum(n)) and isprime(r+digsum(r))): end: A191221 := proc(n) option remember: local k: if(n=1)then return 1: fi: for k from procname(n-1)+1 do if(isA191221(k))then return k: fi: od: end: seq(A191221(n), n=1..57); # Nathaniel Johnston, May 27 2011

Mathematica

nrQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Total[idn]; And@@PrimeQ[{n+t, FromDigits[Reverse[idn]]+t}]]; Select[Range[1200], nrQ] (* Harvey P. Dale, Feb 24 2013 *)

Crossrefs

Cf. A004086, A007953.

Sequence in context: A296862 A225079 A214790 * A216996 A165265 A329818

Adjacent sequences: A191218 A191219 A191220 * A191222 A191223 A191224

Keyword

nonn,base,easy

Author

Carmine Suriano, May 27 2011

Status

approved