A084194 -id:A084194 - cp's OEIS frontend

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

Patrick Capelle, Jun 20 2003

Note that 137 and 139 are twin primes.

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

			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.

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

Subset of A084194/2.

Cf. A007953, A049084.

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

Select[Prime[Range[300]],And@@PrimeQ[Total/@{IntegerDigits[#], IntegerDigits[2 #]}]&] (* Harvey P. Dale, Jun 26 2011 *)
Select[Prime[Range[500]],AllTrue[{Total[IntegerDigits[#]],Total[IntegerDigits[2#]]},PrimeQ]&] (* Harvey P. Dale, Jan 27 2025 *)

More terms from Reinhard Zumkeller, Jun 26 2003

Offset changed to 1 by Robert Israel, Sep 04 2019

A084195 Even numbers n such that the sum of the digits is prime, n/2 is prime and the sum of the digits of n/2 is also prime.

Original entry on oeis.org

14, 58, 94, 122, 166, 274, 278, 302, 346, 382, 386, 454, 458, 526, 562, 566, 634, 674, 706, 746, 818, 922, 926, 1114, 1154, 1198, 1202, 1282, 1286, 1466, 1514, 1594, 1642, 1646, 1774, 1822, 1954, 2038, 2078, 2102, 2182, 2186, 2218, 2258, 2326, 2362

Offset: 1

Patrick Capelle, Jun 20 2003

			5+8=13 for n=58 and 2+9=11 for n/2=29=prime.
1+2+2=5 for n=122 and 6+1=7 for n/2=61=prime.
2+7+8=17 for n=278 and 1+3+9=13 for n/2=139=prime.

Subsequence of A084194.

isok(n) = {if (n % 2, return (0)); dn = digits(n); dh = digits(n/2); isprime(n/2) && isprime(sum(i=1, #dn, dn[i])) && isprime(sum(i=1, #dh, dh[i]));} \\ Michel Marcus, Aug 12 2013

More terms from Michel Marcus, Aug 12 2013

cp's OEIS Frontend

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

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