A178092 -id:A178092 - cp's OEIS frontend

A178091 Emirps whose digital sums are also emirps.

157, 179, 337, 359, 733, 751, 953, 971, 1097, 1237, 1259, 1381, 1439, 1453, 1471, 1583, 1619, 1723, 1741, 1831, 3019, 3109, 3163, 3257, 3271, 3343, 3347, 3433, 3527, 3541, 3613, 3851, 7253, 7321, 7433, 7523, 7699, 7879, 7901, 9013, 9103, 9161, 9341, 9521, 9679, 9769, 9787, 9967

Offset: 1

Lekraj Beedassy, May 19 2010

Palindromic primes are not allowed, nor are palindromic digital sums of primes. - Harvey P. Dale, Feb 23 2014

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Silva, Prime Curios, Entry 157.

Cf. A006567, A178092, A178093.

dseQ[n_]:=Module[{idn=IntegerDigits[n],ds},ds=IntegerDigits[Total[idn]];idn!=Reverse[idn]&&ds!=Reverse[ds] && And@@PrimeQ[{FromDigits[ Reverse[ idn]],FromDigits[ds],FromDigits[Reverse[ds]]}]]; Select[Prime[Range[ 1300]],dseQ] (* Harvey P. Dale, Feb 23 2014 *)

A178093 Larger of emirp pairs whose digital sums are also emirps (A178091).

Original entry on oeis.org

733, 751, 953, 971, 1741, 1831, 3271, 3433, 3541, 3613, 3851, 7253, 7321, 7433, 7523, 7901, 9013, 9103, 9161, 9341, 9521, 9769, 9787, 9967, 13711, 14431, 14831, 15241, 15511, 15601, 15731, 16451, 17041, 18701, 19421, 30271, 30491, 30851, 31081, 31481, 31531, 32341

Offset: 1

Lekraj Beedassy, May 19 2010

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A109309, A178091, A178092.

emirpQ[n_] := n != IntegerReverse[n] && PrimeQ[n] && PrimeQ[IntegerReverse[n]]; q[n_] := emirpQ[DigitSum[n]] && n > IntegerReverse[n] && emirpQ[n]; Select[Range[10^5], q] (* Amiram Eldar, Apr 30 2024 *)

More terms from Amiram Eldar, Apr 30 2024

A230255 Emirps whose sum of digits is prime.

Original entry on oeis.org

113, 157, 179, 199, 311, 337, 359, 733, 739, 751, 937, 953, 971, 991, 1031, 1033, 1091, 1097, 1103, 1109, 1181, 1213, 1217, 1231, 1237, 1259, 1279, 1301, 1321, 1381, 1439, 1453, 1471, 1499, 1523, 1583, 1619, 1657, 1723, 1741, 1811, 1831, 1901, 1949, 3011, 3019

Offset: 1

K. D. Bajpai, Oct 14 2013

			a(6)= 337 is emirp. Sum of digits= 3+3+7= 13 which is prime.
a(11)= 937 is emirp. Sum of digits= 9+3+7= 19 which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..8500

Cf. A006567 (emirps: primes whose reversal is different prime).
Cf. A082806 (palindromic primes: sum of digits is prime).
Cf. A178092 (emirps: digital sum is emirp).

with(StringTools):KD:= proc() local a,b,d; a:=ithprime(n);b:=parse(Reverse(convert(a,string))); d:=add( i,i = convert((a), base, 10))(a);if a<>b and isprime(b) and isprime(d) then return(a):fi; end: seq(KD(),n=1..2000);

Select[Prime[Range[500]],!PalindromeQ[#]&&AllTrue[{IntegerReverse[#],Total[ IntegerDigits[ #]]},PrimeQ]&] (* Harvey P. Dale, Nov 01 2022 *)

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A178091 Emirps whose digital sums are also emirps.

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A178093 Larger of emirp pairs whose digital sums are also emirps (A178091).

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A230255 Emirps whose sum of digits is prime.

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