A092528 -id:A092528 - cp's OEIS frontend

A111525 a(1) = 10; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

10, 1, 3, 3, 3, 29, 1, 3, 3, 11, 9, 7, 23, 61, 11, 3, 91, 137, 7, 11, 31, 93, 17, 9, 273, 51, 397, 9, 99, 41, 111, 129, 111, 801, 109, 131, 297, 37, 621, 21, 807, 143, 87, 57, 231, 187, 53, 169, 77, 613, 867, 41, 199, 773, 523, 227, 27, 499, 171, 329, 67, 483, 393, 179

Offset: 1

Amarnath Murthy, Jason Earls and Robert G. Wilson v, Aug 05 2005

Cf. A111524, A074346, A092528, A069603, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A111525.

a[1] = 10; a[n_] := a[n] = Block[{k = 1, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 63}]

A069602 a(1) = 1; a(n) = smallest composite number such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

1, 9, 9, 9, 21, 9, 51, 21, 9, 57, 301, 51, 51, 33, 209, 111, 87, 153, 121, 87, 63, 39, 77, 27, 57, 81, 129, 147, 111, 21, 147, 321, 69, 93, 153, 621, 817, 129, 81, 803, 129, 153, 451, 171, 717, 801, 959, 459, 187, 291, 231, 533, 399, 291, 289, 869, 489, 171, 381, 667, 21

Offset: 1

Amarnath Murthy, Mar 26 2002

			a(5) = 21 and the number 199921 is a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..200

Cf. A033680, A074336, A092528.

a[1] = 1; a[n_] := a[n] = Block[{k = 3, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[PrimeQ[k] || !PrimeQ[FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 61}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{jx_,a_}]:=Module[{c=9},While[PrimeQ[c]||CompositeQ[jx*10^IntegerLength[c]+c],c+=2];{jx*10^IntegerLength[c]+c,c}]; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Feb 08 2025 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 31 2003

A069604 a(1) = 1; for n>1, a(n) = smallest number with all odd digits giving a prime in concatenation with the previous terms.

Original entry on oeis.org

1, 1, 3, 11, 1, 3, 3, 53, 13, 39, 9, 3, 399, 11, 9, 133, 3, 11, 51, 111, 13, 53, 31, 3, 173, 1, 317, 519, 579, 1, 573, 357, 5111, 39, 51, 73, 3317, 1977, 5173, 579, 357, 359, 9, 57, 3991, 959, 951, 7, 111, 1959, 39, 191, 3357, 3151, 3137, 577, 117, 1353, 951, 153, 99

Offset: 1

Amarnath Murthy, Mar 26 2002

			a(5) = 1 and the number 113111 is a prime.

Cf. A033680, A074336, A092528, A069602.

a[1] = 1; a[n_] := a[n] = Block[{k = 1, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ Union[ Mod[ IntegerDigits[k], 2]] != {1} || !PrimeQ[ FromDigits[ Join[ Flatten[c], IntegerDigits[k]]]], k = k + 1]; k]; Table[ a[n], {n, 61}] (* corrected by Jason Yuen, Jun 22 2025 *)

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

A110435 Beginning with 11, least number such that every partial concatenation is a prime.

Original entry on oeis.org

11, 3, 11, 1, 3, 3, 53, 13, 39, 9, 3, 21, 53, 79, 11, 19, 59, 27, 49, 21, 23, 211, 153, 189, 3, 161, 121, 167, 183, 193, 77, 21, 349, 107, 129, 343, 119, 241, 143, 37, 77, 31, 159, 183, 531, 1517, 7, 59, 159, 123, 9, 1513, 203, 343, 59, 9, 999

Offset: 1

Amarnath Murthy, Aug 03 2005

As n tends to infinity, does everyy term in A045572 arise infinitely many often and with same frequency? - Stefan Steinerberger, Feb 05 2006

			11,113,11311,113111,1131113,11311133 are all prime.

a(n)=A092528(n+1), n>1. [From R. J. Mathar, Aug 18 2008]

More terms from Stefan Steinerberger, Feb 05 2006

cp's OEIS Frontend

A111525 a(1) = 10; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A069602 a(1) = 1; a(n) = smallest composite number such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A069604 a(1) = 1; for n>1, a(n) = smallest number with all odd digits giving a prime in concatenation with the previous terms.

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A110435 Beginning with 11, least number such that every partial concatenation is a prime.

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