A243586 -id:A243586 - cp's OEIS frontend

A166561 Primes p such that sum of digits + 1 is prime.

2, 11, 13, 19, 31, 37, 73, 79, 97, 101, 103, 109, 127, 163, 181, 211, 271, 277, 307, 349, 367, 433, 439, 457, 499, 523, 541, 547, 613, 619, 631, 673, 691, 709, 727, 769, 787, 811, 853, 859, 877, 907, 967, 1009

Offset: 1

Vincenzo Librandi, Oct 28 2009

			2 belongs to this sequence because 2+1=3 prime; 11 because 1+1+1=3; 127 because 1+2+7+1=11; 1009 because 1+0+0+9+1=11.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A243586.

[p: p in PrimesUpTo(1500) | IsPrime(q) where q is 1+(&+Intseq(p))]; // Vincenzo Librandi, Jun 07 2014

Select[Prime[Range[210]], PrimeQ[Plus @@IntegerDigits[#] + 1]&] (* Vincenzo Librandi, Sep 15 2013 *)

A176985 Primes p such that sum of digits + 5 is prime.

Original entry on oeis.org

2, 11, 17, 53, 59, 71, 101, 107, 149, 167, 233, 239, 251, 257, 293, 347, 383, 419, 431, 491, 503, 509, 521, 563, 617, 653, 701, 743, 761, 941, 1049, 1061, 1151, 1193, 1223, 1229, 1283, 1319, 1373, 1409, 1427, 1481, 1511, 1553, 1571, 1601, 1607, 1733

Offset: 1

Vincenzo Librandi, Apr 30 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A243586.

[p: p in PrimesUpTo(1500) | IsPrime(q) where q is 5+&+Intseq(p)]; // Vincenzo Librandi, Jun 07 2014

Select[Prime[Range[2000]], PrimeQ[Plus@@IntegerDigits[#] + 5] &] (* Vincenzo Librandi, Feb 15 2014 *)

A243587 Primes p such that sum of digits + 7 is prime.

Original entry on oeis.org

13, 19, 31, 37, 73, 79, 97, 103, 109, 127, 163, 181, 211, 271, 277, 307, 349, 367, 433, 439, 457, 499, 523, 541, 547, 613, 619, 631, 673, 691, 709, 727, 769, 787, 811, 853, 859, 877, 907, 967, 1009, 1021, 1063, 1069, 1087, 1117, 1153, 1171, 1201, 1249, 1399

Offset: 1

Vincenzo Librandi, Jun 07 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A243586.

[p: p in PrimesUpTo(1500) | IsPrime(q) where q is 7+(&+Intseq(p))];

Select[ Prime[Range[600]], PrimeQ[Plus@@IntegerDigits[#] + 7] &]

A243588 Primes p such that sum of digits + 9 is prime.

Original entry on oeis.org

2, 11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 101, 103, 107, 109, 127, 149, 163, 167, 181, 211, 233, 239, 251, 257, 271, 293, 307, 347, 383, 389, 419, 431, 433, 479, 491, 499, 503, 509, 521, 523, 541, 563, 569, 587, 613, 617, 631, 653, 659, 677, 701, 743

Offset: 1

Vincenzo Librandi, Jun 07 2014

Robert Israel and Vincenzo Librandi, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Vincenzo Librandi)

Cf. similar sequences listed in A243586.

[p: p in PrimesUpTo(1500) | IsPrime(q) where q is 9+&+Intseq(p)];

filter:= n -> isprime(convert(convert(n,base,10),`+`)+9):
select(isprime and filter,[$1..1000]); # Robert Israel, Jun 08 2014

Select[Prime[Range[200]], PrimeQ[Plus@@IntegerDigits[#] + 9] &]

A253848 Primes p such that the digit sums of p, p + 4 and p^2 + 4 are all prime.

Original entry on oeis.org

43, 61, 151, 197, 199, 397, 601, 661, 733, 823, 883, 1051, 1093, 1123, 1297, 1381, 1453, 1471, 1543, 1831, 1873, 2281, 2371, 2551, 2683, 2713, 2953, 2971, 3181, 3343, 3361, 3583, 3613, 3631, 4003, 4153, 4261, 4513, 4603, 4621, 4801, 4951, 5011, 5101, 5323, 5413

Offset: 1

K. D. Bajpai, Jan 16 2015

			a(1) = 43: 43+4 = 47; 43^2+4 = 1853. Their digit sums 4+3 = 7, 4+7 = 11 and 1+8+5+3 = 17 are all prime.
a(2) = 61: 61+4 = 65; 61^2+4 = 3725. Their digit sums 6+1 = 7, 6+5 = 11 and 3+7+2+5 = 17 are all prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A076162, A243586.

digsum:= n -> convert(convert(n,base,10),`+`):
select(p -> isprime(p) and isprime(digsum(p)) and isprime(digsum(p+4)) and isprime(digsum(p^2+4)), [2,seq(2*k+1, k=1..10^4)]); # Robert Israel, Jan 16 2015

k = 4; Select[Prime[Range[1, 2000]], PrimeQ[Plus @@ IntegerDigits[#]] && PrimeQ[Plus @@ IntegerDigits[k+#]] && PrimeQ[Plus @@ IntegerDigits[k+#^2]] &]
Select[Prime[Range[800]],AllTrue[Total/@IntegerDigits[{#,#+4,#^2+4}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 14 2015 *)

for( n=1, 10^2, p=prime(n);  k=4; if(isprime(eval(Str(sumdigits(p)))) & isprime(eval(Str(sumdigits(p+k)))) &isprime(eval(Str(sumdigits(p^2+k)))), print1(p,"  ",) ) )

forprime(p=1,10000,if(isprime(sumdigits(p)) && isprime(sumdigits(p+4)) && isprime(sumdigits(p^2+4)),print1(p", "))) \\ Dana Jacobsen, Sep 07 2015

use ntheory ":all"; forprimes { say if is_prime(sumdigits($)) && is_prime(sumdigits($+4)) && is_prime(sumdigits($*$+4)) } 1000; # Dana Jacobsen, Sep 07 2015

cp's OEIS Frontend

A166561 Primes p such that sum of digits + 1 is prime.

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Magma

Mathematica

A176985 Primes p such that sum of digits + 5 is prime.

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Magma

Mathematica

A243587 Primes p such that sum of digits + 7 is prime.

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Magma

Mathematica

A243588 Primes p such that sum of digits + 9 is prime.

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Magma

Maple

Mathematica

A253848 Primes p such that the digit sums of p, p + 4 and p^2 + 4 are all prime.

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Maple

Mathematica

PARI

PARI

Perl