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A176600 Numbers n such that concatenations n//13 and n//31 are consecutive primes. 2
19, 190, 250, 346, 378, 400, 402, 456, 516, 553, 567, 586, 664, 759, 762, 853, 931, 972, 1140, 1156, 1161, 1242, 1266, 1284, 1314, 1317, 1338, 1398, 1440, 1645, 1744, 1785, 1840, 1875, 1930, 1944, 2227, 2248, 2271, 2287, 2316, 2397, 2401, 2467, 2568, 2602 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
p = n//13 = n * 10^2 + 13 = prime(i) , q = n//31 = n * 10^2 + 31 = prime(i+1)
p and q are formed by the same digits (counted with multiplicity)
n = m//k (k = 0, 1, ...,9)
List of m < 10^3
0//13: 19, 25, 40, 114, 144, 184, 193, 280, 411, 415, 567, 604, 634, 777, 852, 862, 870, 943 (18)
1//13: 93, 116, 227, 240, 392, 462, 543, 570, 611, 675, 689, 734, 759, 821, 822, 878, 969, 986 (18)
2//13: 40, 76, 97, 124, 260, 338, 365, 415, 505, 545, 599, 625, 788, 809 (14)
3//13: 55, 85, 312, 349, 421, 424, 451, 454, 619, 622, 724, 928 (12)
4//13: 66, 128, 131, 174, 194, 293, 345, 414, 657, 687, 702, 741, 752, 867, 870, 939 (16)
5//13: 164, 178, 187, 277, 379, 416, 481, 536, 754, 824, 935, 974, 995 (13)
6//13: 34, 45, 51, 58, 115, 126, 231, 336, 402, 432, 439, 489, 502, 541, 705, 780, 838, 850, 909, 985 (20)
7//13: 56, 131, 222, 228, 239, 246, 309, 480, 530, 716, 732, 747, 761, 792, 831, 936, 981 (17)
8//13: 37, 133, 139, 224, 256, 286, 301, 304, 497, 518, 550, 559, 562, 728, 856, 907 (16)
9//13: 1, 75, 526, 558, 681, 720, 765, 916, 943 (9)
The sequence could be defined as "Numbers n such that 100n+13 and 100n+31 are consecutive primes". In that sense it could be considered to be independent of the decimal numeral system. - M. F. Hasler, Dec 04 2010
LINKS
EXAMPLE
19//13 = 1913 = prime(293), 19//31 = 1931 = prime(294), 19 is 1st term
190//13 = 19013 = prime(2161), 190//31 = 19031 = prime(2162), 190 is 2nd term
MATHEMATICA
Select[Range[3000], PrimeQ[# 100+13]&&NextPrime[# 100+13]==# 100+31&] (* Harvey P. Dale, Jun 23 2022 *)
PROG
(PARI) A176600(n, print_all=0)={ for(k=1, 1e9, isprime(100*k+13) | next; nextprime(100*k+17)==100*k+31|next; print_all & print1(k", "); n-- | return(k))} \\ M. F. Hasler, Dec 04 2010
CROSSREFS
Sequence in context: A161512 A162347 A161879 * A139619 A121039 A162639
KEYWORD
base,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 21 2010
STATUS
approved

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Last modified April 22 00:17 EDT 2024. Contains 371886 sequences. (Running on oeis4.)