A069606 -id:A069606 - cp's OEIS frontend

A074340 a(1) = 5; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

5, 9, 23, 37, 39, 47, 57, 97, 119, 187, 257, 271, 273, 281, 309, 367, 449, 529, 687, 759, 933, 1031, 1131, 1237, 1263, 1343, 1731, 1861, 2177, 2337, 2589, 2607, 2743, 3191, 3199, 3281, 3499, 3807, 3867, 4133, 6079, 6189, 6593, 7207, 7479, 7523, 8569, 8571

Offset: 1

Zak Seidov, Sep 23 2002

Michael S. Branicky, Table of n, a(n) for n = 1..411

Cf. A069606, A046254, A074336, A074338, A074339, A074341, A074342, A074343, A074344, A074345, A074346.

a[1] = 5; 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 *)

from sympy import isprime
def aupton(terms):
  alst, astr = [5], "5"
  while len(alst) < terms:
    an = alst[-1] + 2
    while an%5 ==0 or not isprime(int(astr + str(an))): an += 2
    alst, astr = alst + [an], astr + str(an)
  return alst
print(aupton(48)) # Michael S. Branicky, May 09 2021

More terms from Robert G. Wilson v, Aug 05 2005

A074341 a(1) = 4; 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

4, 7, 9, 11, 81, 87, 109, 117, 123, 129, 201, 389, 429, 441, 771, 811, 831, 1037, 1143, 1299, 1569, 1581, 1803, 1837, 1943, 2053, 2171, 2379, 2431, 3201, 3437, 3489, 3723, 3841, 4289, 4801, 5523, 6249, 7083, 7467, 7749, 8171, 9073, 9333, 9683, 9781, 10833

Offset: 1

Zak Seidov, Sep 23 2002

Harvey P. Dale, Table of n, a(n) for n = 1..100

Cf. A033679, A033680, A033681.

Cf. A069606, A046254, A074336, A074338, A074339, A074340, A074342, A074343, A074344, A074345, A074346.

a[1] = 4; 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, 47}] (* Robert G. Wilson v *)
nxt[{j_,a_}]:=Module[{k=a+1},While[!PrimeQ[j*10^IntegerLength[k]+k],k++];{j*10^IntegerLength[k]+k,k}]; NestList[nxt,{4,4},50][[;;,2]] (* Harvey P. Dale, Apr 07 2025 *)

More terms from Robert G. Wilson v, Aug 05 2005

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

Original entry on oeis.org

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}]

A069621 a(1) = 9; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

9, 97, 197, 1973, 31973, 319733, 3319733, 331973311, 6331973311, 633197331131, 5633197331131, 563319733113127, 6563319733113127, 65633197331131279, 3465633197331131279, 346563319733113127933, 18346563319733113127933

Offset: 1

Amarnath Murthy, Mar 27 2002

			a(4) = 1973 starting with a(3) =197 and a(5) = 31973 ending in a(4) = 1973.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616, A069617, A069618, A069619, A069620.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

A264738 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is triangular (m*(m+1)/2).

Original entry on oeis.org

1, 5, 3, 181, 88028, 21235051740, 567915201450407862150, 344114043575504570099838908555592732193828, 2517587700386740093077985318903210991887701682095104296188806385635425261250603998340

Offset: 1

Anders Hellström, Nov 22 2015

Jon E. Schoenfield, Table of n, a(n) for n = 1..12
Wikipedia, Triangular_number

Cf. A000217, A069606.

istriangular(n)=ispolygonal(n,3)
first(m)=my(v=vector(m),s="1");v[1]=1;for(i=2,m,n=1;while(!istriangular(eval(concat(s,Str(n)))),n++);v[i]=n;s=concat(s,Str(n)));v

a(6)-a(9) from Jon E. Schoenfield, Nov 22 2015

A069613 a(1) = 1; a(2n) is smallest prime starting with a(2n-1) and a number with no insignificant zeros, and a(2n+1) is smallest prime ending in a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

1, 11, 211, 2111, 22111, 2211127, 12211127, 122111279, 14122111279, 1412211127927, 211412211127927, 21141221112792721, 1321141221112792721, 132114122111279272169, 27132114122111279272169, 2713211412211127927216947

Offset: 1

Amarnath Murthy, Mar 27 2002

a(6) is not 2211109 because the 0 in this number is considered insignificant (for comparison, the 0 in 22111109 would be significant, but this value is not the smallest possible extension of a(5)=22111). - Sean A. Irvine, May 07 2024

			a(4) = 2111 starting with a(3) =211 and a(5) = 22111 ending in a(4) = 2111.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069614.

More terms from Robert Gerbicz, Aug 27 2002

Name clarified by Sean A. Irvine, May 07 2024

A069615 a(1) = 3; a(2n) = smallest prime starting (in the most significant digits) with a(2n-1) (i.e., as a right concatenation of a(2n-1) and a number with no insignificant zeros); a(2n+1) = smallest prime ending in (the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

3, 31, 131, 1319, 21319, 213193, 12213193, 122131939, 1122131939, 112213193957, 27112213193957, 271122131939573, 3271122131939573, 327112213193957339, 2327112213193957339, 232711221319395733969, 13232711221319395733969

Offset: 1

Amarnath Murthy, Mar 27 2002

			a(4) = 1319 starting with a(3) = 131 and a(5) = 21319 ending in a(4) = 1319.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

A069616 a(1) = 4; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

4, 41, 241, 2411, 32411, 324113, 6324113, 63241133, 1563241133, 15632411339, 815632411339, 81563241133919, 281563241133919, 2815632411339191, 322815632411339191, 32281563241133919151, 432281563241133919151

Offset: 1

Amarnath Murthy, Mar 27 2002

			a(4) = 2411 starting with a(3) =241 and a(5) = 32411 ending in a(4) = 2411.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

A069617 a(1) = 5; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

5, 53, 353, 3533, 33533, 3353321, 113353321, 1133533213, 101133533213, 10113353321311, 310113353321311, 3101133533213117, 143101133533213117, 14310113353321311739, 314310113353321311739, 314310113353321311739103

Offset: 1

Amarnath Murthy, Mar 27 2002

			a(4) = 3533 starting with a(3) = 353 and a(5) = 33533 ending in a(4) = 3533.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

A069618 a(1) = 6; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

Original entry on oeis.org

6, 61, 461, 46133, 246133, 2461337, 22461337, 224613371, 12224613371, 1222461337117, 151222461337117, 15122246133711733, 615122246133711733, 615122246133711733213, 9615122246133711733213, 961512224613371173321349

Offset: 1

Amarnath Murthy, Mar 27 2002

			a(4) = 46133 starting with a(3) = 461 and a(5) = 246133 in a(4) = 46133.

Cf. A053582, A069605, A069606, A069607, A069608, A069609, A069610, A069611, A069613, A069614, A069615, A069616, A069617.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

cp's OEIS Frontend

A074340 a(1) = 5; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A074341 a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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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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A069621 a(1) = 9; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n). Alternate left and right concatenation yielding primes.

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A264738 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is triangular (m*(m+1)/2).

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A069613 a(1) = 1; a(2n) is smallest prime starting with a(2n-1) and a number with no insignificant zeros, and a(2n+1) is smallest prime ending in a(2n-1). Alternate left and right concatenation yielding primes.

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A069616 a(1) = 4; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

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A069617 a(1) = 5; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

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A069618 a(1) = 6; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.

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