A258183
Numbers which divide the concatenation of the two surrounding primes.
Original entry on oeis.org
7, 9, 49, 111, 1090909, 28571427, 111111111, 3333333327, 25641025641, 10576923076923, 59090909090909, 2631578947368421, 4827586206896549, 8947368421052631, 18644067796610169, 111111111111111111, 812499999999999999, 1889250814332247557, 9189189189189189189
Offset: 1
The number 9 is in the sequence because the surrounding primes are 7 and 11 and 711 is divisible by 9.
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Select[Range[3, 10^4], Divisible[ FromDigits[ Join@@ IntegerDigits@ NextPrime[#, {-1, 1}]], #]&]
A258184
Numbers which divide the concatenation of the next two primes.
Original entry on oeis.org
1, 3, 7, 61, 167, 801, 1143, 2001, 6001, 8001, 125001, 25000001, 181818181819, 2500000000001, 16666666666667, 45000000000001, 640000000000001, 1142857142857143, 4000000000000001, 37500000000000001, 153846153846153847, 937500000000000001, 2881355932203389831
Offset: 1
The number 7 is in the sequence since the next two primes are 11 and 13 and 1113 is divisible by 7.
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Select[Range[10^5], Divisible[ FromDigits[ Join@@ IntegerDigits@ NextPrime[#, {1, 2}]], #]&]
A385536
Integers k formed by the concatenation of 3 consecutive prime numbers such that k is divisible by at least one of those 3 primes.
Original entry on oeis.org
235, 357, 71113, 374143, 616771, 167173179, 143914471451, 909071909089909091, 104651162787110465116278991046511627907
Offset: 1
235 is a term, since it is the concatenation of the consecutive primes 2, 3, 5 and is divisible by 5.
2, 3 and 5: 235 = 5*47
3, 5, and 7: 357 = 3*119 = 7*51
7, 11 and 13: 71113 = 7*10159
37, 41 and 43: 374143 = 43*8701
61, 67 and 71: 616771 = 61*10111
167, 173 and 179: 167173179 = 167*1001037
1439, 1447 and 1451: 143914471451 = 1447*99457133
909071, 909089 and 909091: 909071909089909091 = 909091*999979000001
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tcat:= proc(a,b,c)
c + (b + 10^(1+ilog10(b))*a)*10^(1+ilog10(c))
end proc:
R:= NULL: count:= 0:
q:= 2: r:= 3:
while count < 8 do
p:= q; q:= r; r:= nextprime(r);
x:= tcat(p,q,r);
if igcd(x,p*q*r)>1 then
R:= R,x; count:= count+1;
fi
od:
R; # Robert Israel, Jul 06 2025
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cat[s_] := FromDigits[Flatten[IntegerDigits[s]]]; q[s_] := AnyTrue[s, Divisible[cat[s], #] &]; cat /@ Select[Partition[Prime[Range[72000]], 3, 1], q] (* Amiram Eldar, Jul 03 2025 *)
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