A204672
Primes followed by a gap of 120.
Original entry on oeis.org
1895359, 2898239, 6085441, 7160227, 7784039, 7803491, 7826899, 8367397, 8648557, 9452959, 10052071, 10863973, 11630503, 11962823, 12109697, 12230233, 12415681, 14411737, 14531899, 15014557, 15020737, 15611909, 16179041
Offset: 1
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N = 2*10^7; % to get all terms <= N
P = primes(N+120);
J = find(P(2:end) - P(1:end-1) == 120);
P(J) % Robert Israel, Feb 28 2017
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Transpose[Select[Partition[Prime[Range[1100000]],2,1],Last[#]-First[#] == 120&]] [[1]] (* Harvey P. Dale, Jul 11 2014 *)
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g=120;c=o=0;forprime(p=1,default(primelimit),(-o+o=p)==g&write("c:/temp/b204672.txt",c++" "p-g))
A380785
Smallest of two consecutive primes p and q, both ending with 1, such that q - p = 10n, or -1 if no such primes exist.
Original entry on oeis.org
181, 13421, 4831, 25261, 95651, 43331, 175141, 1060781, 404851, 1648081, 2597981, 6085441, 22151281, 10270451, 25180321, 79817581, 84549821, 135045091, 306099181, 529811591, 164710681, 707429491, 965524181, 391995431, 428045491, 1516828721, 4272226951, 2337682591
Offset: 1
a(1) = 181, because 181 and 181 + 10 = 191 are two consecutive primes with the same last digit 1 and no smaller p has this property.
A224472
Primes followed by a gap of 300.
Original entry on oeis.org
4758958741, 5612345261, 6169169561, 6306815239, 6646984159, 7335508261, 8645089003, 8806019249, 9047808247, 9148138313, 9466071347, 9907846261, 10055451683, 11063821453, 11475026363, 11603081459, 12292390637, 12750876857, 13833827471, 14636472007, 15876700949
Offset: 1
Cf.
A058193 (first gap of 6n),
A140791 (first gap of 10n),
A126771 (gap 60),
A126724 (gap 150),
A204673 (gap 180),
A204807 (gap 200),
A000230,
A001359,
A204672,
A029710,
A031924-
A031938,
A061779,
A098974,
A124594-
A124596,
A126784,
A134116-
A134124,
A204665-
A204670.
A381372
Smaller of two consecutive primes p and q, both ending with 3, such that q-p = 10n, or -1 if no such primes exist.
Original entry on oeis.org
283, 3413, 7253, 19333, 45893, 142993, 399283, 542603, 818723, 396733, 3240983, 10863973, 32788543, 8917523, 17652013, 92593183, 80935103, 92510963, 257789053, 481691513, 20831323, 47326693, 607010093, 1461724573, 387096133, 1496441363, 2298026803, 1855047163
Offset: 1
a(1) = 283, because 283 and 283 + 10 = 293 are two consecutive primes with the same last digit 3 and no smaller p has this property.
A381510
Smaller of two consecutive primes p and q, both ending with 7, such that q - p = 10n, or -1 if no such primes exist.
Original entry on oeis.org
337, 887, 4297, 33247, 31907, 124367, 218287, 1122287, 1964987, 1313467, 1468277, 7160227, 5518687, 16525757, 13626257, 71880637, 27915737, 17051707, 394059907, 566348087, 252314747, 472865287, 1289694257, 633418787, 1588640437, 944192807, 1391048047, 7059848287
Offset: 1
a(1) = 337, because 337 and 337 + 10 = 347 are two consecutive primes with the same last digit 7 and no smaller prime has this property.
-
a(n) = my(p=7); while (!isprime(p) || ((nextprime(p+1)-p) != 10*n), p+=10); p; \\ Michel Marcus, Feb 25 2025
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from sympy import nextprime, isprime
def A381510(n):
p = 17
while (q:=nextprime(p)):
if q-p == 10*n:
return p
p = q+9-(q+2)%10
while not isprime(p):
p += 10 # Chai Wah Wu, Mar 09 2025
A224522
Least prime which is followed by a gap of 30n.
Original entry on oeis.org
4297, 43331, 404851, 1895359, 13626257, 17051707, 20831323, 391995431, 1391048047, 4758958741, 6291356009, 20068818197, 53241805651, 82490815123, 63816175447, 482423533897, 2209016910131, 738832927927, 4442109925217, 4872634110067, 12644461143649, 10653514291843, 15712145060693, 111113196467011
Offset: 1
-
o=2;g=30;forprime(p=3,,(o+g != o=p) & next; print1(p-g",");g+=30) \\ Warning: this code assumes that the sequence is increasing, which may not be the case. - M. F. Hasler, Apr 09 2013
A381511
Smaller of two consecutive primes p and q, both ending with 9, such that q - p = 10*n, or -1 if no such primes exist.
Original entry on oeis.org
139, 3089, 5749, 20809, 60539, 110359, 173359, 618719, 1294849, 838249, 6877109, 1895359, 11188759, 7621259, 35560009, 33803689, 124956059, 92801029, 142414669, 378043979, 229316459, 390932389, 1095750599, 995151679, 2174082649, 2603726969, 3402493709, 1997191249
Offset: 1
a(1) = 139, because 139 and 139 + 10 = 149 are two consecutive primes with the same last digit 9 and no smaller p has this property.
-
a(n) = my(p=9); while (!isprime(p) || ((nextprime(p+1)-p) != 10*n), p+=10); p; \\ Michel Marcus, Feb 25 2025
-
from sympy import isprime, nextprime
def A381511(n):
p = 19
while (q:=nextprime(p)):
if q-p == 10*n:
return p
p = q+9-(q%10)
while not isprime(p):
p += 10 # Chai Wah Wu, Mar 08 2025
Showing 1-7 of 7 results.
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