cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A074344 a(1) = 8; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

8, 9, 23, 51, 69, 81, 93, 129, 169, 179, 181, 273, 321, 323, 471, 493, 633, 689, 781, 933, 951, 969, 1229, 1309, 1509, 1707, 1821, 1863, 1913, 2169, 2337, 2433, 3259, 3513, 3681, 3921, 4431, 4611, 5043, 5091, 5361, 5409, 6231, 6471, 6999, 7757, 7963, 8283
Offset: 1

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Author

Zak Seidov, Sep 23 2002

Keywords

Crossrefs

Cf. A046258, A069610, A074336, A074338, A074339, A074340, A074341, A074342, A074343, A074345, A074346.

Programs

  • Mathematica
    a[1] = 8; a[n_] := a[n] = Block[{k = a[n - 1] + 1 + Mod[a[n - 1], 2], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 48}] (* Robert G. Wilson v *)

Extensions

Corrected and extended by Robert G. Wilson v, Aug 05 2005

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

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

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

Links

Crossrefs

Cf. A033680, A074336, A092528.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

Amarnath Murthy, Mar 26 2002

Keywords

Examples

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

Crossrefs

Cf. A033680, A074336, A092528, A069602.

Programs

  • Mathematica
    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 *)

Extensions

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

A164967 Sequential primes built off of 1.

Original entry on oeis.org

1, 13, 137, 13711, 1371113, 137111329, 13711132937, 13711132937113, 13711132937113307, 13711132937113307401, 13711132937113307401463, 13711132937113307401463509, 13711132937113307401463509541, 13711132937113307401463509541701
Offset: 1

Views

Author

Rajesh Bhowmick, Jan 14 2012

Keywords

Comments

Begin with a 'seed' number, in this case a(1) = 1. Then a(n) is the concatenation of a(n-1) and some prime greater than any prime previously used to create a new prime number. Such a sequence is called a 'sequential prime' sequence.

Links

Crossrefs

Cf. A074336.

Programs

  • Mathematica
    p = 3; f[n_] := Block[{}, While[q = n*10^Floor[1 + Log10[p]] + p; !PrimeQ[q], p = NextPrime[p]]; p = NextPrime[p]; q]; NestList[f, 1, 14] (* Robert G. Wilson v, Jan 14 2012 *)

Extensions

Edited and extended by Robert G. Wilson v, Jan 14 2012

A239547 a(1) = 1; a(n) is smallest number > a(n-1) such that the juxtaposition a(n)a(n-1)...a(1) is a prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 14, 21, 43, 56, 96, 141, 178, 180, 198, 263, 271, 315, 347, 352, 471, 530, 565, 588, 707, 711, 793, 812, 850, 887, 952, 1083, 1214, 1218, 1266, 1564, 1661, 1686, 1744, 1976, 2047, 2066, 2166, 2268, 2412, 2740, 2777, 2895, 2905, 3056, 3058, 3293
Offset: 1

Views

Author

Paolo P. Lava, Mar 21 2014

Keywords

Links

Crossrefs

Cf. A033680, A074336.

Programs

  • Maple
    with(numtheory);
S:=proc(s) local w; w:=convert(s, base, 10); sum(w[j], j=1..nops(w)); end:
T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, j, n; a:=1; j:=2; print(1);
for n from 1 to q do b:=T(a); c:=j*10^b+a;
if isprime(c) then a:=j*10^b+a; print(j); fi;
j:=j+1; od; print(); end: P(10^10);
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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