A050716 -id:A050716 - cp's OEIS frontend

A050719 Inserting a digit '9' between adjacent digits of n makes a prime.

11, 13, 17, 19, 23, 37, 41, 49, 53, 59, 61, 77, 91, 97, 131, 157, 167, 169, 173, 181, 191, 193, 197, 211, 227, 239, 259, 307, 311, 319, 323, 337, 349, 371, 379, 413, 419, 427, 431, 433, 449, 457, 467, 481, 491, 493, 499, 503, 517, 533, 539, 547, 563, 569, 571

Offset: 1

Patrick De Geest, Aug 15 1999

			181 becomes 1(9)8(9)1 which is prime 19891.

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Cf. A050674, A050711, A050712, A050713, A050714, A050716, A050717, A050718, A050719.

Select[Range[10,1000],PrimeQ[FromDigits[Riffle[IntegerDigits[#],9]]]&] (* Harvey P. Dale, Oct 29 2014 *)

Offset changed to 1 by Georg Fischer, Oct 15 2019

A050674 Inserting a digit '0' between adjacent digits of n makes a prime.

Original entry on oeis.org

11, 13, 17, 19, 37, 41, 49, 53, 59, 61, 67, 71, 79, 89, 97, 107, 109, 113, 131, 133, 151, 161, 167, 179, 193, 199, 211, 217, 221, 247, 257, 259, 277, 287, 289, 293, 313, 319, 323, 337, 343, 359, 373, 377, 383, 389, 409, 457, 469, 479, 481, 493, 511, 527, 553

Offset: 1

Patrick De Geest, Aug 15 1999

			373 becomes 3(0)7(0)3 which is prime 30703.

Cf. A050711, A050712, A050713, A050715, A050716, A050717, A050718, A050719.

(* This program works in Mathematica 6.0 and later *)
Select[Range[11, 1000,2], PrimeQ[FromDigits[Riffle[IntegerDigits[#], 0]]] &] (* T. D. Noe, Dec 22 2010 *)
(* The following program has been tested in Mathematica 5.1 and it works *)
Reap[c = 0; d = 0; Do[If[MemberQ[{1, 3, 7, 9}, Mod[n, 10]], id = IntegerDigits[n]; Do[id[[k]] = {id[[k]], d}, {k, Length[id] - 1}]; If[PrimeQ[FromDigits[Flatten[id]]], Sow[n]; c++; If[c > 999, Break[]]]], {n, 11, 20000}]][[2,1]] (* Zak Seidov, Dec 22 2010 *)

Offset set to 1 by Georg Fischer, Oct 15 2019

A050711 Inserting a digit '1' between adjacent digits of n makes a prime.

Original entry on oeis.org

13, 21, 31, 33, 37, 49, 63, 67, 69, 79, 81, 91, 99, 113, 117, 119, 123, 131, 137, 141, 159, 167, 177, 179, 183, 201, 203, 207, 209, 221, 233, 237, 239, 249, 257, 261, 263, 267, 273, 287, 291, 303, 309, 329, 339, 351, 353, 357, 387, 401, 407, 413, 417, 423

Offset: 1

Patrick De Geest, Aug 15 1999

			303 becomes 3(1)0(1)3 which is prime 31013.

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Cf. A050674, A050712, A050713, A050714, A050715, A050716, A050717, A050718, A050719.

Select[Range[10,500],PrimeQ[FromDigits[Riffle[IntegerDigits[#],1]]]&] (* Harvey P. Dale, Apr 25 2019 *)

is(n) = if(gcd(10, n%10) > 1 || n < 10, return(0)); my(d = digits(n), v = vector(2*#d - 1, i, if(i % 2 == 1, d[i>>1 + 1], 1))); isprime(fromdigits(v)) \\ David A. Corneth, Oct 15 2019

Offset set to 1 by Georg Fischer, Oct 15 2019

A050712 Inserting a digit '2' between adjacent digits of n makes a prime.

Original entry on oeis.org

17, 23, 27, 29, 41, 51, 53, 77, 81, 83, 87, 89, 99, 127, 133, 139, 141, 157, 171, 181, 183, 189, 193, 207, 213, 219, 229, 261, 271, 277, 291, 307, 309, 331, 333, 337, 343, 349, 361, 403, 421, 423, 427, 433, 477, 481, 489, 493, 499, 501, 507, 511, 517, 523

Offset: 1

Patrick De Geest, Aug 15 1999

			333 becomes 3(2)3(2)3 which is prime 32323.

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Cf. A050674, A050711, A050713, A050714, A050715, A050716, A050717, A050718, A050719.

Select[Range[10,600],PrimeQ[FromDigits[Riffle[IntegerDigits[#],2]]]&] (* Harvey P. Dale, Sep 13 2014 *)

Offset changed to 1 by Georg Fischer, Oct 15 2019

A050713 Inserting a digit '3' between adjacent digits of n makes a prime.

Original entry on oeis.org

11, 17, 19, 23, 29, 31, 37, 41, 43, 49, 61, 73, 79, 89, 97, 103, 107, 131, 137, 139, 157, 163, 181, 191, 193, 209, 211, 233, 239, 241, 251, 257, 259, 263, 281, 283, 307, 331, 353, 367, 379, 391, 397, 407, 413, 427, 431, 463, 493, 521, 523, 529, 547, 563, 569

Offset: 1

Patrick De Geest, Aug 15 1999

			407 becomes 4(3)0(3)7 which is prime 43037.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A050674, A050711, A050712, A050714, A050715, A050716, A050717, A050718, A050719.

Select[Range[10,600],PrimeQ[FromDigits[Riffle[IntegerDigits[#],3]]]&] (* Harvey P. Dale, Dec 23 2023 *)

A050714 Inserting a digit '4' between adjacent digits of n makes a prime.

Original entry on oeis.org

19, 21, 37, 39, 43, 49, 51, 57, 61, 63, 67, 73, 91, 97, 113, 119, 123, 129, 131, 137, 147, 149, 153, 159, 171, 177, 183, 197, 203, 209, 227, 243, 257, 279, 281, 287, 293, 311, 317, 353, 359, 369, 377, 381, 383, 387, 389, 399, 401, 429, 449, 453, 459, 461, 467

Offset: 1

Patrick De Geest, Aug 15 1999

			389 becomes 3(4)8(4)9 which is prime 34849.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A050674, A050711, A050712, A050713, A050715, A050716, A050717, A050718, A050719.

Select[Range[10,500],PrimeQ[FromDigits[Riffle[IntegerDigits[#],4]]]&] (* Harvey P. Dale, Nov 03 2024 *)

A050717 Inserting a digit '7' between adjacent digits of n makes a prime.

Original entry on oeis.org

13, 19, 21, 27, 33, 39, 49, 51, 57, 63, 67, 73, 87, 91, 97, 107, 137, 141, 147, 153, 159, 191, 197, 203, 207, 219, 221, 227, 249, 263, 273, 279, 311, 323, 327, 339, 351, 353, 359, 381, 389, 429, 477, 479, 497, 503, 507, 513, 519, 521, 533, 551, 569, 573, 593

Offset: 1

Patrick De Geest, Aug 15 1999

			E.g. 477 becomes 4(7)7(7)7 which is prime 47777.

Cf. A050674, A050711, A050712, A050713, A050714, A050716, A050717, A050718, A050719.

Select[Range[10, 500], PrimeQ[FromDigits[Riffle[IntegerDigits[#], 7]]]&] (* Georg Fischer, Oct 15 2019 after Harvey P. Dale *)

Offset changed to 1 by Georg Fischer, Oct 15 2019

A050715 Inserting a digit '5' between adjacent digits of n makes a prime.

Original entry on oeis.org

11, 17, 21, 27, 33, 39, 47, 57, 63, 69, 71, 77, 83, 87, 89, 93, 103, 129, 139, 141, 151, 159, 189, 199, 207, 213, 223, 237, 243, 247, 267, 279, 291, 301, 303, 309, 313, 319, 321, 327, 333, 373, 379, 381, 391, 403, 429, 453, 457, 469, 471, 477, 483, 493, 499

Offset: 1

Patrick De Geest, Aug 15 1999

			373 becomes 3(5)7(5)3 which is prime 35753.

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Cf. A050674, A050711, A050712, A050713, A050714, A050716, A050717, A050718, A050719.

Select[Range[10,500],PrimeQ[FromDigits[Riffle[IntegerDigits[#],5]]]&] (* Harvey P. Dale, Apr 07 2018 *)

Offset changed to 1 by Georg Fischer, Oct 15 2019

A331116 Inserting a digit '1' between the first two adjacent digits of k, then inserting a digit '2' between the two following adjacent digits of k, ..., then inserting the integer '10' between the tenth and the eleventh digits of k, ... produces a prime number.

Original entry on oeis.org

13, 21, 31, 33, 37, 49, 63, 67, 69, 79, 81, 91, 99, 107, 131, 139, 143, 157, 161, 181, 187, 193, 197, 203, 211, 221, 227, 233, 251, 253, 259, 277, 281, 299, 311, 313, 323, 331, 337, 367, 371, 373, 377, 379, 403, 421, 427, 451, 461, 467, 479

Offset: 1

Bernard Schott, Jan 10 2020

Inspired by the sequences A050711 to A050719, so the first 13 terms are the first 13 terms of A050711, then a(14) = 107 because 1(1)0(2)7 gives 11027 which is a prime.

			281 gives 2(1)8(2)1 = 21821 that is prime, hence 281 is a term.
1027 gives 1(1)0(2)2(3)7 = 1102237 that is prime, hence 1027 is another term.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A050711, A050712, A050713, A050714.

Cf. A050715, A050716, A050717, A050718, A050719.

seqQ[n_] := PrimeQ @ FromDigits @ Flatten @ IntegerDigits @ Riffle[(d = IntegerDigits[n]), Range[Length[d] - 1]]; Select[Range[10,480], seqQ] (* Amiram Eldar, Jan 10 2020 *)

from sympy import isprime
def ok(n):
    if n < 10: return False
    s = str(n)
    shuffle = list(map(str, ((i+1)//2 for i in range(2*len(s)-1))))
    shuffle[0::2] = [s[i] for i in range(len(s))]
    return isprime(int("".join(shuffle)))
print(list(filter(ok, range(480)))) # Michael S. Branicky, Jul 18 2021

cp's OEIS Frontend

A050719 Inserting a digit '9' between adjacent digits of n makes a prime.

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A050674 Inserting a digit '0' between adjacent digits of n makes a prime.

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A050711 Inserting a digit '1' between adjacent digits of n makes a prime.

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A050712 Inserting a digit '2' between adjacent digits of n makes a prime.

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A050713 Inserting a digit '3' between adjacent digits of n makes a prime.

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A050714 Inserting a digit '4' between adjacent digits of n makes a prime.

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A050717 Inserting a digit '7' between adjacent digits of n makes a prime.

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Extensions

A050715 Inserting a digit '5' between adjacent digits of n makes a prime.

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Programs

Mathematica

Extensions

A331116 Inserting a digit '1' between the first two adjacent digits of k, then inserting a digit '2' between the two following adjacent digits of k, ..., then inserting the integer '10' between the tenth and the eleventh digits of k, ... produces a prime number.

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