A083966 -id:A083966 - cp's OEIS frontend

A092115 Duplicate of A083966.

1, 6, 8, 9, 16, 17, 18, 21, 23, 24, 29, 32, 39, 64, 70, 78, 84, 85, 98, 1000, 1005, 1013

Offset: 1

dead

A032711 Numbers k such that k prefixed by '2' and followed by '3' is prime.

2, 3, 6, 8, 9, 11, 14, 15, 20, 21, 24, 27, 29, 33, 38, 39, 42, 47, 50, 54, 59, 63, 66, 68, 69, 71, 75, 80, 83, 84, 90, 95, 96, 101, 102, 114, 116, 119, 128, 131, 132, 138, 143, 149, 150, 152, 156, 161, 167, 168, 171, 177, 180, 186, 189, 194, 200, 201, 206, 207, 209

Offset: 1

Patrick De Geest, May 15 1998

This sequence is infinite, a consequence of the Prime Number Theorem in arithmetic progressions. - Charles R Greathouse IV, Sep 26 2012

			8 and 21 are in the sequence because 283 and 2213 are primes.

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

Cf. A032702-A032733.

Cf. A083677, A083966, A083969, A092117.

v={};Do[If[PrimeQ[FromDigits[Join[{2},IntegerDigits[n],{3}]]], v=Append[v,n]],{n, 260}];v (* Farideh Firoozbakht, Jun 15 2003 *)
Select[Range[210],PrimeQ[FromDigits[Join[{2},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, May 02 2012 *)

for( n=1,300, isprime(eval(Str(2,n,3))) & print1(n",")) \\ M. F. Hasler, Mar 18 2008

Merged with data from duplicate entry A092114. - M. F. Hasler, Mar 18 2008

A083677 Define f(n, k) to be the concatenation of the first n primes, with n-1 k's inserted between the primes. Then a(n) is the smallest k >= 0 such that f(n, k) is prime, or -1 if no such prime exists.

Original entry on oeis.org

0, 2, -1, 1, 4, 10, 38, 20, 0, -1, 163, 46, 8, 53, 0, -1, 74, 5, 8, 5, 180, 4, 280, 191, 0, 337, 191, -1, 105, 88, 19, 28, 111, -1, 525, 13, 24, 102, 159, -1, 288, 142, 31, 743, 81, -1, 183, 202, 100, 96, 380, -1, 1227, 5, 113, 123, 20, 23, 0, 48, 148, 438, 52, 144, 128, 297, 206

Offset: 1

Farideh Firoozbakht, Jun 15 2003

a(3) = -1 because f(3, k) is always a multiple of 5. For any n such that n = 1 (mod 3) and A007504(n) = 0 (mod 3), a(n) = -1 because f(n, k) is always a multiple of 3. It is my conjecture that for all other n, -1 < a(n) < n*p(n). I've checked for all n < 270.

			a(4) = 1 because 2030507 is composite and 2131517 is prime.

C. Rivera, On Solution Of Puzzle 208 .

A082549 gives the n such that a(n) = 0. A083684 gives the n such that a(n)=-1.

Cf. A082549, A032711, A083966, A083969, A092117, A090529.

fpkQ[k_, n_] := PrimeQ[ FromDigits[ Flatten[ IntegerDigits /@ Insert[ Table[ Prime[i], {i, k}], n, Table[{i}, {i, 2, k}]]]]]; a[1] = 0; a[3] = a[10] = a[16] = a[28] = a[34] = a[40] = a[46] = a[52] = a[70] = a[76] = a[82] = a[88] = a[97] = -1; a[n_] := Block[{k = 0}, While[ fpkQ[n, k] != True, k++ ]; k]; Table[ a[n], {n, 70}] (* Robert G. Wilson v, Dec 11 2004 *)

Edited and extended by Robert G. Wilson v, Dec 11 2004

A092117 Numbers n such that the concatenation 2n3n5n7n11n13 is prime.

Original entry on oeis.org

10, 43, 51, 55, 58, 60, 136, 171, 204, 213, 214, 222, 270, 288, 309, 334, 339, 364, 366, 376, 414, 423, 460, 477, 492, 501, 502, 507, 513, 519, 565, 585, 586, 597, 621, 649, 726, 729, 787, 852, 861, 870, 903, 906, 915, 933, 946, 981, 988, 1005, 1038, 1071

Offset: 1

Farideh Firoozbakht, Jun 15 2003

This concatenation is fp(6, n) as defined in A083677.

			10 is in the sequence because 210310510710111013 is prime.

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

Cf. A032711, A083677, A083966, A083677, A092115, A083969.

v={};Do[If[PrimeQ[FromDigits[Join[{2}, IntegerDigits[n], {3}, IntegerDigits[n], {5}, IntegerDigits[n], {7}, IntegerDigits[n], {1, 1}, IntegerDigits[n], {1, 3}]]], v=Append[v, n]], {n, 1400}];v
fp6Q[n_] := PrimeQ[ FromDigits[ Flatten[ IntegerDigits /@ Insert[{2, 3, 5, 7, 11, 13}, n, {{2}, {3}, {4}, {5}, {6}}]]]]; Select[ Range[1100], fp6Q[ # ] &] (* Robert G. Wilson v, Dec 11 2004 *)
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@Riffle[{2,3,5,7,11,13}, #]]]]&] (* Harvey P. Dale, Mar 21 2013 *)

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007

cp's OEIS Frontend

A092115 Duplicate of A083966.

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A032711 Numbers k such that k prefixed by '2' and followed by '3' is prime.

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A083677 Define f(n, k) to be the concatenation of the first n primes, with n-1 k's inserted between the primes. Then a(n) is the smallest k >= 0 such that f(n, k) is prime, or -1 if no such prime exists.

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A092117 Numbers n such that the concatenation 2n3n5n7n11n13 is prime.

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