A069614
a(1) = 2; a(2n) = smallest prime starting (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
2, 23, 223, 2237, 32237, 3223729, 63223729, 632237297, 2632237297, 263223729721, 12263223729721, 1226322372972173, 171226322372972173, 17122632237297217381, 2117122632237297217381, 21171226322372972173813
Offset: 1
a(4) = 2111 starting with a(3) = 211 and a(5) = 22111 ending in a(4) = 2111.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003
A053583
a(n+1) is the smallest prime ending with (but not equal to) a(n), where a(1)=3.
Original entry on oeis.org
3, 13, 113, 2113, 12113, 612113, 11612113, 1611612113, 111611612113, 1111611612113, 81111611612113, 2181111611612113, 132181111611612113, 11132181111611612113, 3411132181111611612113, 413411132181111611612113, 12413411132181111611612113
Offset: 1
-
A[1]:= 3;
for n from 2 to 100 do
d:= 10^(ilog10(A[n-1])+1);
for k from 1 do
p:= A[n-1]+d*k;
if isprime(p) then
A[n]:= p;
break
fi
od
od:
seq(A[n],n=1..100); # Robert Israel, Jul 15 2014
-
from sympy import isprime
from itertools import count, islice
def agen(an=3):
while True:
yield an
pow10 = 10**len(str(an))
for t in count(pow10+an, step=pow10):
if isprime(t):
an = t
break
print(list(islice(agen(), 17))) # Michael S. Branicky, Jun 23 2022
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
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
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
a(4) = 2111 starting with a(3) =211 and a(5) = 22111 ending in a(4) = 2111.
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
a(4) = 1319 starting with a(3) = 131 and a(5) = 21319 ending in a(4) = 1319.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003
A053584
a(n+1) is the smallest prime ending with a(n), where a(1)=7.
Original entry on oeis.org
7, 17, 317, 6317, 26317, 126317, 2126317, 72126317, 372126317, 5372126317, 125372126317, 15125372126317, 415125372126317, 23415125372126317, 2223415125372126317, 152223415125372126317, 21152223415125372126317, 4221152223415125372126317
Offset: 1
-
from sympy import isprime
from itertools import count, islice
def agen(an=7):
while True:
yield an
pow10 = 10**len(str(an))
for t in count(pow10+an, step=pow10):
if isprime(t):
an = t
break
print(list(islice(agen(), 18))) # Michael S. Branicky, Jun 23 2022
A069612
a(1) = 19 (the smallest prime ending in a 9) and a(n+1) = smallest prime ending in a(n).
Original entry on oeis.org
19, 419, 5419, 35419, 435419, 11435419, 111435419, 9111435419, 89111435419, 1389111435419, 81389111435419, 381389111435419, 15381389111435419, 3315381389111435419, 153315381389111435419, 22153315381389111435419, 2022153315381389111435419
Offset: 1
-
w=9; Table[w; i=1; While[PrimeQ[ToExpression[StringJoin[ToString[i], ToString[w]]]]==False, i++ ]; w=ToExpression[StringJoin[ToString[i], ToString[w]]], {32}]
nxt[n_]:=Module[{c=10^IntegerLength[n],x=1},While[!PrimeQ[c*x+n],x++];c*x+n]; NestList[nxt,19,15] (* Harvey P. Dale, Sep 25 2013 *)
-
from sympy import isprime
from itertools import count, islice
def agen(an=19):
while True:
yield an
pow10 = 10**len(str(an))
for t in count(pow10+an, step=pow10):
if isprime(t):
an = t
break
print(list(islice(agen(), 17))) # Michael S. Branicky, Jun 23 2022
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
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
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
A077714
a(1) = 1; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.
Original entry on oeis.org
1, 11, 211, 4211, 34211, 234211, 4234211, 304234211, 9304234211, 209304234211, 7209304234211, 37209304234211, 3037209304234211, 23037209304234211, 323037209304234211, 70000323037209304234211, 300070000323037209304234211, 600300070000323037209304234211
Offset: 1
a(8) = 304234211; deleting 3 gives 4234211 = a(7).
-
a:= proc(n) option remember; local k, m, d, p;
if n=1 then 1 else k:= a(n-1);
for m from length(k) do
for d to 9 do p:= k +d*10^m;
if isprime(p) then return p fi
od od
fi
end:
seq(a(n), n=1..20); # Alois P. Heinz, Jan 12 2015
-
from sympy import isprime
from itertools import islice
def agen(an=1):
while True:
yield an
pow10 = 10**len(str(an))
while True:
found = False
for t in range(pow10+an, 10*pow10+an, pow10):
if isprime(t):
an = t; found = True; break
if found: break
pow10 *= 10
print(list(islice(agen(), 18))) # Michael S. Branicky, Jun 23 2022
Showing 1-10 of 15 results.
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