A199683 -id:A199683 - cp's OEIS frontend

A056807 Numbers k such that 3*10^k + 1 is prime.

1, 3, 7, 10, 28, 36, 67, 81, 147, 483, 643, 1020, 1900, 2620, 10453, 27720, 52824, 105589, 111988, 618853, 665829

Offset: 1

Robert G. Wilson v, Aug 22 2000

			k = 3 gives (3*10^3+1) = 3000+1 = 3001, which is prime.

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]
Makoto Kamada, Prime numbers of the form 300...001.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A056797, A062339, A101823, A199683, A259866.

Do[ If[ PrimeQ[ 3*10^k + 1], Print[ k ]], {k, 0, 20000}]

is(k)=isprime(3*10^k+1) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = A101823(n) + 1.

a(13)-a(14) from Julien Peter Benney (jpbenney(AT)ftml.net), Nov 23 2004
a(15) from Hugo Pfoertner, Jan 18 2005
a(16)-a(17) from Robert G. Wilson v, Jan 18 2005
a(18) from Roman Makarchuk, Dec 05 2008 confirmed as next term by Ray Chandler, Mar 02 2012
a(19) from Alexander Gramolin, Feb 24 2012 confirmed as next term by Ray Chandler, Mar 02 2012
a(20)-a(21) from Kamada data by Robert Price, Jan 26 2015

A349278 a(n) is the product of the sum of the last i digits of n, with i going from 1 to the total number of digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 0, 4, 10, 18, 28, 40, 54, 70, 88, 108, 0, 5, 12, 21, 32, 45, 60, 77, 96, 117, 0, 6, 14, 24, 36, 50, 66, 84, 104, 126, 0, 7, 16, 27, 40, 55, 72, 91, 112, 135, 0

Offset: 1

Michel Marcus, Nov 13 2021

This is similar to A349194 but with digits taken in reversed order.
The only primes in the sequence are 2, 3, 5 and 7. - Bernard Schott, Dec 04 2021
The positive terms form a subsequence of A349194. - Bernard Schott, Dec 19 2021

			For n=256, a(256) = 6*(6+5)*(6+5+2) = 858.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A349194, A349279 (fixed points).

Cf. A349864, A349865.

a[n_] := Times @@ Accumulate @ Reverse @ IntegerDigits[n]; Array[a, 70] (* Amiram Eldar, Nov 13 2021 *)

a(n) = my(d=Vecrev(digits(n))); prod(i=1, #d, sum(j=1, i, d[j]));

from math import prod
from itertools import accumulate
def a(n): return 0 if n%10==0 else prod(accumulate(map(int, str(n)[::-1])))
print([a(n) for n in range(1, 71)]) # Michael S. Branicky, Nov 13 2021

From Bernard Schott, Dec 04 2021: (Start)
a(n) = 0 iff n is a multiple of 10 (A008592).
a(n) = 1 iff n = 1.
a(n) = 2 (resp. 3, 4, 5, 7, 9) iff n = 10^k+1 (A000533) (resp. 2*10^k+1 (A199682), 3*10^k+1 (A199683), 4*10^k+1 (A199684), 6*10^k+1 (A199686), 8*10^k+1 (A199689)).
a(R_n) = n! where R_n = A002275(n) is repunit > 0, and n! = A000142(n).
a(n) = A349194(n) if n is palindrome (A002113). (End)

A259866 Primes of the form 3*10^k + 1.

Original entry on oeis.org

31, 3001, 30000001, 30000000001, 30000000000000000000000000001, 3000000000000000000000000000000000001, 30000000000000000000000000000000000000000000000000000000000000000001

Offset: 1

N. J. A. Sloane, Jul 08 2015

nonn

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.
S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]

Cf. A199683, A056807, A062339.

Select[3*10^Range[70]+1,PrimeQ] (* Harvey P. Dale, Jul 05 2020 *)

a(n) = 3*10^A056807(n)+1. - R. J. Mathar, Jul 15 2015

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A056807 Numbers k such that 3*10^k + 1 is prime.

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A349278 a(n) is the product of the sum of the last i digits of n, with i going from 1 to the total number of digits of n.

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A259866 Primes of the form 3*10^k + 1.

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Author

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Programs

Mathematica

Formula