A008864 -id:A008864 - cp's OEIS frontend

A175224 a(n) = prime(n) + 8.

10, 11, 13, 15, 19, 21, 25, 27, 31, 37, 39, 45, 49, 51, 55, 61, 67, 69, 75, 79, 81, 87, 91, 97, 105, 109, 111, 115, 117, 121, 135, 139, 145, 147, 157, 159, 165, 171, 175, 181, 187, 189, 199, 201, 205, 207, 219, 231, 235, 237, 241, 247, 249, 259, 265, 271, 277, 279

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

a(n) = A000040(n) + 8 = A008864(n) + 7 = A052147(n) + 6 = A113395(n) + 5 = A175221(n) + 4 = A175222(n) + 3 = A139049(n) + 2 = A175223(n) + 1 = A140353(n) - 1 = A175225(n) - 2.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A008864, A052147, A113395, A175221, A175222, A139049, A175223, A140353, A175225.

Filtered([1..300], k-> IsPrime(k) ) + 8; # G. C. Greubel, May 20 2019

[(p+8): p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

Prime[Range[60]]+8 (* Harvey P. Dale, Mar 02 2015 *)

{a(n) = prime(n) + 8}; \\ G. C. Greubel, May 20 2019

[nth_prime(n) + 8 for n in (1..60)] # G. C. Greubel, May 20 2019

More terms from Vincenzo Librandi, Mar 14 2010

A175225 a(n) = prime(n) + 10.

Original entry on oeis.org

12, 13, 15, 17, 21, 23, 27, 29, 33, 39, 41, 47, 51, 53, 57, 63, 69, 71, 77, 81, 83, 89, 93, 99, 107, 111, 113, 117, 119, 123, 137, 141, 147, 149, 159, 161, 167, 173, 177, 183, 189, 191, 201, 203, 207, 209, 221, 233, 237, 239, 243, 249, 251, 261, 267, 273, 279, 281

Offset: 1

Jaroslav Krizek, Mar 06 2010

nonn

a(n) = A000040(n) + 10 = A008864(n) + 9 = A052147(n) + 8 = A113395(n) + 7 = A175221(n) + 6 = A175222(n) + 5 = A139049(n) + 4 = A175223(n) + 3 = A175224(n) + 2 = A140353(n) + 1.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A008864, A052147, A113395, A139049, A140353, A175221, A175222, A175223, A175224.

Filtered([1..300], k-> IsPrime(k) ) + 10; # G. C. Greubel, May 21 2019

[(p+10):p in PrimesUpTo(500)]; // Vincenzo Librandi, Dec 04 2010

10 + Prime[Range[70]] (* G. C. Greubel, May 21 2019 *)

{a(n) = prime(n) + 10}; \\ G. C. Greubel, May 21 2019

[nth_prime(n) + 10 for n in (1..70)] # G. C. Greubel, May 21 2019

More terms from Vincenzo Librandi, Mar 14 2010

A239708 Numbers of the form m = 2^i + 2^j, where i > j >= 0, such that m - 1 is prime.

Original entry on oeis.org

3, 6, 12, 18, 20, 24, 48, 68, 72, 80, 132, 192, 258, 264, 272, 384, 1032, 1040, 1088, 1152, 1280, 2064, 2112, 4100, 4112, 4128, 4160, 5120, 6144, 8448, 16448, 20480, 32772, 32784, 32832, 33024, 33792, 65538, 65540, 65544, 65552, 65600, 66048, 73728, 81920, 262148, 262152, 262272, 262400, 263168, 266240, 294912, 524352, 528384, 786432

Offset: 1

Hieronymus Fischer, Mar 27 2014

nonn

Complement of the disjunction of A079696 with A187813. This means that a number m is a term if and only if b = 2 is the only base for which the base-b digital sum of m is b.

			a(1) = 3, since 3 = 2^1 + 2^0.
a(3) = 12, since 12 = 2^3 + 2^2.

Hieronymus Fischer, Table of n, a(n) for n = 1..250

Cf. A239709 - A239720.

Cf. A239703, A187813, A079696, A008864.

from itertools import islice
from sympy import isprime
def A239708_gen(): # generator of terms
    yield (n:=3)
    while True:
        n = n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b
        if isprime(n-1):
            yield n
A239708_list = list(islice(A239708_gen(),30)) # Chai Wah Wu, Mar 24 2025

A239708
"Answers the n-th term of A239708.
  Usage: n A239708
  Answer: a(n)"
  | a b i k m p q terms |
  terms := OrderedCollection new.
  b := 2.
  p := 1.
  k := 0.
  m := 0.
  [k < self] whileTrue:
         [m := m + 1.
         p := b * p.
         q := 1.
         i := 0.
         [i < m and: [k < self]] whileTrue:
                   [i := i + 1.
                   a := p + q.
                   (a - 1) isPrime
                        ifTrue:
                            [k := k + 1.
                            terms add: a].
                   q := b * q]].
  ^terms at: self
-----------------

A239708inv
  "Answers a kind of inverse of A239708.
  Usage: n A239708inv
  Answer: max ( k | A239708(k) < n)"
  | k |
  k := 1.
  [k A239708 < self] whileTrue: [k := k + 1].
  ^k - 1

A239703(a(n)) = 1.

A286623 Square array A(n,k) = A276943(n,k)/A002110(n-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 3, 1, 4, 4, 1, 5, 6, 6, 1, 7, 7, 10, 8, 1, 9, 16, 11, 14, 12, 1, 10, 19, 36, 15, 22, 14, 1, 11, 21, 41, 78, 23, 26, 18, 1, 13, 22, 45, 85, 144, 27, 34, 20, 1, 15, 31, 46, 91, 155, 222, 35, 38, 24, 1, 16, 34, 71, 92, 165, 235, 324, 39, 46, 30, 1, 17, 36, 76, 155, 166, 247, 341, 438, 47, 58, 32, 1, 18, 37, 80, 162, 287, 248, 357, 457, 668, 59, 62, 38, 1

Offset: 1

Antti Karttunen, Jun 28 2017

			The top left 12 X 12 corner of the array:
  1,  3,  4,  5,    7,    9,   10,   11,   13,   15,   16,   17
  1,  4,  6,  7,   16,   19,   21,   22,   31,   34,   36,   37
  1,  6, 10, 11,   36,   41,   45,   46,   71,   76,   80,   81
  1,  8, 14, 15,   78,   85,   91,   92,  155,  162,  168,  169
  1, 12, 22, 23,  144,  155,  165,  166,  287,  298,  308,  309
  1, 14, 26, 27,  222,  235,  247,  248,  443,  456,  468,  469
  1, 18, 34, 35,  324,  341,  357,  358,  647,  664,  680,  681
  1, 20, 38, 39,  438,  457,  475,  476,  875,  894,  912,  913
  1, 24, 46, 47,  668,  691,  713,  714, 1335, 1358, 1380, 1381
  1, 30, 58, 59,  900,  929,  957,  958, 1799, 1828, 1856, 1857
  1, 32, 62, 63, 1148, 1179, 1209, 1210, 2295, 2326, 2356, 2357
  1, 38, 74, 75, 1518, 1555, 1591, 1592, 3035, 3072, 3108, 3109

Transpose: A286625.
Cf. A002110, A276943.
Row 1: A276155.
Column 1: A000012, Column 2: A008864, Column 3: A100484, Column 4: A072055, Column 5: A023523 (from its second term onward), Column 6: A286624 (= 1 + A123134), Column 11: 2*A123134, Column 13: 3*A006094.
Cf. A276616 (analogous array).

(define (A286623 n) (A286623bi (A002260 n) (A004736 n)))
(define (A286623bi row col) (/ (A276943bi row col) (A002110 (- row 1))))

A(n,k) = A276943(n, k) / A002110(n-1).

A286625 Square array A(n,k) = A276945(n,k)/A002110(k-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

1, 1, 3, 1, 4, 4, 1, 6, 6, 5, 1, 8, 10, 7, 7, 1, 12, 14, 11, 16, 9, 1, 14, 22, 15, 36, 19, 10, 1, 18, 26, 23, 78, 41, 21, 11, 1, 20, 34, 27, 144, 85, 45, 22, 13, 1, 24, 38, 35, 222, 155, 91, 46, 31, 15, 1, 30, 46, 39, 324, 235, 165, 92, 71, 34, 16, 1, 32, 58, 47, 438, 341, 247, 166, 155, 76, 36, 17, 1, 38, 62, 59, 668, 457, 357, 248, 287, 162, 80, 37, 18

Offset: 1

Antti Karttunen, Jun 28 2017

			The top left 12 X 12 corner of the array:
   1,  1,  1,   1,   1,   1,   1,   1,    1,    1,    1,    1
   3,  4,  6,   8,  12,  14,  18,  20,   24,   30,   32,   38
   4,  6, 10,  14,  22,  26,  34,  38,   46,   58,   62,   74
   5,  7, 11,  15,  23,  27,  35,  39,   47,   59,   63,   75
   7, 16, 36,  78, 144, 222, 324, 438,  668,  900, 1148, 1518
   9, 19, 41,  85, 155, 235, 341, 457,  691,  929, 1179, 1555
  10, 21, 45,  91, 165, 247, 357, 475,  713,  957, 1209, 1591
  11, 22, 46,  92, 166, 248, 358, 476,  714,  958, 1210, 1592
  13, 31, 71, 155, 287, 443, 647, 875, 1335, 1799, 2295, 3035
  15, 34, 76, 162, 298, 456, 664, 894, 1358, 1828, 2326, 3072
  16, 36, 80, 168, 308, 468, 680, 912, 1380, 1856, 2356, 3108
  17, 37, 81, 169, 309, 469, 681, 913, 1381, 1857, 2357, 3109

Transpose: A286623.
Cf. A002110, A276945.
Column 1: A276155.
Row 1: A000012, Row 2: A008864, Row 3: A100484, Row 4: A072055, Row 5: A023523 (from its second term onward), Row 6: A286624.
Cf. A276617 (analogous array).

(define (A286625 n) (A286625bi (A002260 n) (A004736 n)))
(define (A286625bi row col) (/ (A276945bi row col) (A002110 (- col 1))))

A(n,k) = A276945(n, k) / A002110(k-1).

A299374 Numbers k such that k * 11^k - 1 is prime.

Original entry on oeis.org

2, 8, 252, 1184, 1308

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(6) > 500000.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), this sequence (b=11), A299375 (b=12), A299376 (b=13), A299377 (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*11^n-1)];

Select[Range[1, 10000], PrimeQ[n*11^n-1] &]

for(n=1, 10000, if(ispseudoprime(n*11^n-1), print1(n", ")))

A299375 Numbers k such that k * 12^k - 1 is prime.

Original entry on oeis.org

1, 6, 43, 175, 821, 910, 1157, 13748, 27032, 71761, 229918

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(12) > 500000.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), this sequence (b=12), A299376 (b=13), A299377 (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*12^n-1)];

Select[Range[1, 10000], PrimeQ[n*12^n-1] &]

for(n=1, 10000, if(isprime(n*12^n-1), print1(n", ")))

A299376 Numbers k such that k * 13^k - 1 is prime.

Original entry on oeis.org

2, 6, 563528

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(4) > 570008.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), A299375 (b=12), this sequence (b=13), A299377 (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*13^n-1)];

Select[Range[1, 10000], PrimeQ[n*13^n-1] &]

for(n=1, 10000, if(isprime(n*13^n-1), print1(n", ")))

A299377 Numbers k such that k * 14^k - 1 is prime.

Original entry on oeis.org

1, 3, 7, 98, 104, 128, 180, 834, 1633, 8000, 28538, 46605, 131941, 147684, 433734

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(16) > 500000.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), A299375 (b=12), A299376 (b=13), this sequence (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*14^n-1)];

Select[Range[1, 10000], PrimeQ[n*14^n-1] &]

for(n=1, 10000, if(isprime(n*14^n-1), print1(n", ")))

A299378 Numbers k such that k * 15^k - 1 is prime.

Original entry on oeis.org

2, 10, 14, 2312, 16718, 26906, 27512, 41260, 45432, 162454, 217606

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(12) > 500000.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), A299375 (b=12), A299376 (b=13), A299377 (b=14), this sequence (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*15^n-1)];

Select[Range[1, 10000], PrimeQ[n*15^n-1] &]

for(n=1, 10000, if(isprime(n*15^n-1), print1(n", ")))

cp's OEIS Frontend

A175224 a(n) = prime(n) + 8.

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A175225 a(n) = prime(n) + 10.

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A239708 Numbers of the form m = 2^i + 2^j, where i > j >= 0, such that m - 1 is prime.

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A286623 Square array A(n,k) = A276943(n,k)/A002110(n-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A286625 Square array A(n,k) = A276945(n,k)/A002110(k-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A299374 Numbers k such that k * 11^k - 1 is prime.

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Magma

Mathematica

PARI

A299375 Numbers k such that k * 12^k - 1 is prime.

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