A176600 Numbers n such that concatenations n//13 and n//31 are consecutive primes.

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

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

Table of n, a(n) for n=1..46.

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

Cf. A168327, A168417, A173836, A174213, A174260, A174355, A174441.

Sequence in context: A161512 A162347 A161879 * A139619 A121039 A162639

Adjacent sequences: A176597 A176598 A176599 * A176601 A176602 A176603

Keyword

base,nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 21 2010

Status

approved