A084201 Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime.

7, 29, 47, 61, 83, 137, 139, 151, 173, 191, 193, 227, 229, 263, 281, 283, 317, 337, 353, 373, 409, 461, 463, 557, 577, 599, 601, 641, 643, 733, 757, 797, 821, 823, 887, 911, 977, 1019, 1039, 1051, 1091, 1093, 1109, 1129, 1163, 1181, 1217, 1237, 1291

Offset

1,1

Comments

Note that 137 and 139 are twin primes.

A049084(A007953(a(n)))*A049084(A007953(2*a(n))) > 0. - Reinhard Zumkeller, Jun 26 2003

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

2+9=11=prime for 29 and 5+8=13=prime for 58=2*29;
1+3+7=11=prime for 137 and 2+7+4=13=prime for 274=2*137;
1+3+9=13=prime for 139 and 2+7+8=17=prime for 278=2*139.

Maple

filter:= proc(n)
  isprime(n) and isprime(convert(convert(n, base, 10), `+`)) and isprime(convert(convert(2*n, base, 10), `+`))
end proc:
select(filter, [seq(i, i=3..5000, 2)]); # Robert Israel, Sep 04 2019

Mathematica

Select[Prime[Range[300]], And@@PrimeQ[Total/@{IntegerDigits[#], IntegerDigits[2 #]}]&] (* Harvey P. Dale, Jun 26 2011 *)

Crossrefs

Subset of A084194/2.

Cf. A007953, A049084.

Sequence in context: A045465 A330723 A165492 * A031380 A005698 A080185

Adjacent sequences: A084198 A084199 A084200 * A084202 A084203 A084204

Keyword

base,nonn

Author

Patrick Capelle, Jun 20 2003

Extensions

More terms from Reinhard Zumkeller, Jun 26 2003

Offset changed to 1 by Robert Israel, Sep 04 2019

Status

approved