A240679 -id:A240679 - cp's OEIS frontend

A240678 Primes p such that p*10+k is prime for exactly one value of the digit k.

11, 29, 41, 47, 71, 79, 83, 131, 137, 139, 151, 163, 173, 181, 191, 227, 257, 263, 277, 281, 293, 307, 311, 313, 359, 383, 449, 491, 503, 509, 557, 563, 569, 577, 587, 593, 601, 617, 647, 659, 661, 677, 683, 719, 739, 743, 751, 809, 821, 827, 857, 877, 881

Offset: 1

Colin Barker, Apr 10 2014

			11 is in the sequence because 113 is prime, but 111, 117 and 119 are not prime.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A067267, A119289, A240679, A240680, A240689.

Select[Prime[Range[200]],Total[Boole[PrimeQ[10 #+{1,3,7,9}]]]==1&] (* Harvey P. Dale, Apr 19 2019 *)

forprime(p=2, 1500, t=0; forstep(k=1, 9, 2, if(isprime(p*10+k), t++)); if(t==1, print1(p, ", ")))

from sympy import isprime, primerange
def ok(p): return sum(1 for k in [1, 3, 7, 9] if isprime(p*10+k)) == 1
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(881)) # Michael S. Branicky, Nov 29 2021

A240680 Primes p such that p*10+k is prime for exactly three values of the digit k.

Original entry on oeis.org

7, 13, 31, 43, 61, 103, 109, 199, 271, 367, 409, 421, 523, 541, 547, 787, 823, 829, 883, 1009, 1033, 1117, 1237, 1291, 1669, 1999, 2131, 2161, 2203, 2269, 2437, 2503, 2593, 2671, 2857, 3049, 3253, 3271, 3361, 3559, 3583, 3769, 3823, 4003, 4201, 4339, 4357

Offset: 1

Colin Barker, Apr 10 2014

			7 is in the sequence because 71, 73 and 79 are prime, but 77 is not prime.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A067267, A119289, A240678, A240679, A240689.

[p: p in PrimesUpTo(10^4) | {k: k in [1,3,7,9] | IsPrime(p*10+k)} in Subsets({1,3,7,9},3)]; // Bruno Berselli, Apr 10 2014

Select[Prime[Range[600]],Total[Boole[PrimeQ[10#+{1,3,7,9}]]]==3&] (* Harvey P. Dale, Apr 07 2023 *)

forprime(p=2, 10000, t=0; forstep(k=1, 9, 2, if(isprime(p*10+k), t++)); if(t==3, print1(p, ", ")))

A240689 The number of values of the digit k for which prime(n)*10+k is prime.

Original entry on oeis.org

2, 2, 2, 3, 1, 3, 2, 4, 2, 1, 3, 2, 1, 3, 1, 0, 2, 3, 2, 1, 2, 1, 1, 0, 2, 2, 3, 0, 3, 0, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 1, 3, 2, 2, 1, 0, 0, 2, 3, 0, 3, 0, 2, 2, 0

Offset: 1

Colin Barker, Apr 10 2014

			a(16) = 0 because prime(16) = 53, and 531, 533, 537 and 539 are not prime.
a(5) = 1 because prime(5) = 11, and 113 is prime, but 111, 117 and 119 are not prime.
a(1) = 2 because prime(1) = 2, and 23 and 29 are prime, but 21 and 27 are not prime.
a(4) = 3 because prime(4) = 7, and 71, 73 and 79 are prime, but 77 is not prime.
a(8) = 4 because prime(8) = 19, and 191, 193, 197 and 199 are all prime.

Colin Barker, Table of n, a(n) for n = 1..10000

Cf. A067267, A119289, A240678, A240679, A240680.

Count[#,?PrimeQ]&/@Table[10*Prime[n]+k,{n,90},{k,{1,3,7,9}}] (* _Harvey P. Dale, Mar 25 2018 *)

forprime(p=2, 10000, t=0; forstep(k=1, 9, 2, if(isprime(p*10+k), t++)); print1(t, ", "))

cp's OEIS Frontend

A240678 Primes p such that p*10+k is prime for exactly one value of the digit k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A240680 Primes p such that p*10+k is prime for exactly three values of the digit k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A240689 The number of values of the digit k for which prime(n)*10+k is prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI