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A084201 Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)