A226099 -id:A226099 - cp's OEIS frontend

A347343 Positive integers k such that k with the last digit repeated is prime.

1, 19, 21, 23, 27, 31, 43, 49, 57, 59, 67, 73, 81, 87, 91, 97, 103, 127, 139, 143, 149, 151, 169, 173, 177, 181, 187, 193, 199, 201, 209, 211, 231, 233, 237, 239, 241, 247, 263, 267, 269, 271, 277, 283, 299, 301, 329, 343, 349, 351, 353, 367, 373, 383, 387

Offset: 1

Paolo Xausa, Aug 27 2021

			21 is a term because 211 is prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A000040, A226099.

upto=500;Select[Range[1,upto,2],PrimeQ[FromDigits[Join[d=IntegerDigits[#],{Last[d]}]]]&]

forprime(p=9,1e4, if(p%100%11==0, print1(p\10", "))) \\ Charles R Greathouse IV, Aug 27 2021

from sympy import isprime
def ok(n): return isprime(10*n + n%10)
print(list(filter(ok, range(388)))) # Michael S. Branicky, Aug 28 2021

a(n) ~ n log n by the prime number theorem in arithmetic progressions. (These numbers are the primes mod 11, 33, 77, or 99 mod 100 with their last digit removed.) - Charles R Greathouse IV, Aug 27 2021

A347344 Positive integers k such that k with the first (most significant) digit repeated is prime.

Original entry on oeis.org

1, 13, 23, 27, 29, 31, 37, 43, 49, 57, 61, 73, 81, 83, 87, 91, 97, 103, 109, 117, 123, 129, 151, 153, 163, 171, 181, 187, 193, 203, 207, 213, 221, 237, 239, 243, 251, 267, 269, 273, 281, 287, 293, 297, 301, 307, 313, 319, 323, 329, 331, 343, 347, 359, 361

Offset: 1

Paolo Xausa, Aug 27 2021

Conjecture: the sequence contains infinitely many twin prime pairs (k, k+2) such that (D(k), D(k+2)) is a twin prime pair, where D(x) = x with the most significant digit repeated. The first such k is 659: both (659, 661) and (6659, 6661) are twin prime pairs. All these k begin with either 3, 6, or 9.

			27 is a term because 227 is prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A000040, A226099, A347343.

upto=500;Select[Range[1,upto,2],PrimeQ[FromDigits[Join[{First[d=IntegerDigits[#]]},d]]]&]

isok(k) = my(d=digits(k)); isprime(eval(fromdigits(concat(d[1], d)))); \\ Michel Marcus, Sep 09 2021

from sympy import isprime
def ok(n): s = str(n); return isprime(int(s[0] + s))
print(list(filter(ok, range(362)))) # Michael S. Branicky, Aug 27 2021

A226100 Main diagonal A(n,n) of matrix A(k,n) = n-th k-th power that becomes prime when its most significant (i.e., leftmost) decimal digit is removed.

Original entry on oeis.org

12, 289, 729, 20151121, 371293, 2839760855281, 24160660561265139, 241100240228887100161, 3421941488772218992567, 845219547726738091164049, 7506514445791062595879589895041, 293936151563356954592299567713259041, 6657844787831219696900816415217242830357

Offset: 1

Jonathan Vos Post, May 26 2013

Row 1 = A(1,n) = A226099. Row 2 = A(2,n) = A225873. Row 3 = A(3,n) = A226090. Row 4 = A(4,n) = A226092. Row 5 = A(5,n) = A226098.

			a(1) = A(1,1) = 12 = first number whose first power (itself) becomes prime when its most significant (or leftmost) digit is removed.
a(2) = A(2,2) = 289 = second square which becomes prime when its most significant (or leftmost) digit is removed.
a(3) =

Cf. A000040, A226099, A225873, A226090, A226092, A226098.

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A347343 Positive integers k such that k with the last digit repeated is prime.

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A347344 Positive integers k such that k with the first (most significant) digit repeated is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A226100 Main diagonal A(n,n) of matrix A(k,n) = n-th k-th power that becomes prime when its most significant (i.e., leftmost) decimal digit is removed.

Views

Author

Keywords

Comments

Examples

Crossrefs