A088291 -id:A088291 - cp's OEIS frontend

A088292 Smallest prime in which the digit string can be partitioned in n+1 parts (0 parts allowed) such that the sum of the first n parts = the (n+1)th one.

11, 101, 1427, 10067, 100517, 1000427, 10000247, 100001147, 1000000427, 10000001057, 100000000427, 1000000002227, 10000000002227, 100000000000067, 1000000000011227, 10000000000002137, 100000000000000337

Offset: 0

Amarnath Murthy, Sep 30 2003

			a(1) = 11, 1 = 1.
a(2) = 167, 1+6 = 7
a(3) = 1427, 1+4+2 = 7.

Cf. A088291, A088293.

More terms from David Wasserman, Aug 04 2005

A088293 Smallest prime in which the digit string can be partitioned into n+1 parts (only nonzero parts allowed) such that the sum of the first n parts = the (n+1)th one.

Original entry on oeis.org

11, 167, 1427, 12227, 111227, 11117213, 11111117, 1111111411, 11111111917, 111111118319, 1111111111717, 11111111132923, 111111111114823, 1111111111113823, 11111111111111923, 111111111111112319, 1111111111111116223, 11111111111111121119, 111111111111111111523

Offset: 1

Amarnath Murthy, Sep 30 2003

			a(1) = 11, 1 = 1.
a(2) = 167, 1+6 = 7
a(3) = 1427, 1+4+2 = 7.
a(4) = 12227, 1+2+2+2 = 7.
a(5) = 111227, 1+1+1+2+2 = 7.
a(6) = 11117213, 1+1+1+1+7+2 = 13.
a(7) = 11111117, 1+1+1+1+1+1+1 = 7.
a(8) = 1111111411, 1+1+1+1+1+1+1+4 = 11.

Cf. A088291, A088292.

a(6)-a(8) from Randy L. Ekl, Jan 08 2017
Offset corrected by Omar E. Pol, Jan 09 2017
a(9)-a(19) from Giovanni Resta, Apr 24 2017

A088294 Primes in which the digit string can be partitioned into three parts such that third (least significant) part is the product of the first two.

Original entry on oeis.org

199, 313, 919, 7321, 7963, 11717, 11777, 12323, 13339, 14747, 15959, 16363, 17117, 17351, 18181, 18787, 21121, 23369, 27127, 29129, 29387, 31393, 31751, 31957, 32369, 32987, 39139, 41141, 47147, 51151, 59159, 71171, 81181, 87187, 89189

Offset: 1

Amarnath Murthy, Sep 30 2003

Primes in A280635. - Randy L. Ekl, Jan 09 2017

			17351 is a member as it can be partitioned as (17, 3, 51) and 17*3 = 51.

Cf. A088291, A088292, A088293, A280635, A280636.

More terms from David Wasserman, Aug 04 2005

Offset changed to 1 by Michel Marcus, Jan 08 2017

A067860 Primes which are the concatenation of numbers n_1, n_2, n_3, in that order, with n_1 + n_2 = n_3 (leading zeros are forbidden for nonzero n_i).

Original entry on oeis.org

101, 167, 257, 347, 617, 5813, 7411, 8311, 8513, 9413, 9817, 10111, 10313, 11213, 11617, 12113, 12517, 12829, 13417, 13619, 14243, 14519, 14923, 15217, 15823, 15859, 16061, 16319, 17623, 18119, 18523, 19423, 19697, 20323, 20929, 21517, 22123, 23537, 23629, 23831, 24547

Offset: 1

Joseph L. Pe, Feb 15 2002

			167 is the concatenation of 1, 6, 7 and 1+6 = 7.

David A. Corneth, Table of n, a(n) for n = 1..10000
David A. Corneth, PARI program

See A088291 for another version.

is(n)=if(n==101, return(1)); my(d=digits(n)); for(i=1,#d-2, for(j=i+1,#d-1, if(digits(fromdigits(d[1..i])+fromdigits(d[i+1..j]))==d[j+1..#d] && (d[i+1] || i==j+1), return(isprime(n))))); 0
select(is,primes(10^4)) \\ Charles R Greathouse IV, Sep 21 2015

\\ See PARI link. David A. Corneth, Mar 06 2021

More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002

Data corrected and more terms from David A. Corneth, Mar 06 2021

A088295 Smallest prime in which the digit string can be partitioned in n+1 parts such that the product of the first n parts = the (n+1)th one.

Original entry on oeis.org

11, 199, 3319, 11177, 111919, 1111339, 11133119, 111111199, 1111111919, 11111113319, 1111111139381, 1111111111177, 11111111113139, 111111111113113, 1111111111113319, 11111111311111319, 111111111311111113

Offset: 0

Amarnath Murthy, Sep 30 2003

			a(3) = 3319 because it can be partitioned as 3, 3, 1, 9 and 3*3*1 = 9.

Cf. A088291, A088292, A088293, A088294.

More terms from David Wasserman, Aug 08 2005

cp's OEIS Frontend

A088292 Smallest prime in which the digit string can be partitioned in n+1 parts (0 parts allowed) such that the sum of the first n parts = the (n+1)th one.

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A088293 Smallest prime in which the digit string can be partitioned into n+1 parts (only nonzero parts allowed) such that the sum of the first n parts = the (n+1)th one.

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A088294 Primes in which the digit string can be partitioned into three parts such that third (least significant) part is the product of the first two.

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A067860 Primes which are the concatenation of numbers n_1, n_2, n_3, in that order, with n_1 + n_2 = n_3 (leading zeros are forbidden for nonzero n_i).

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A088295 Smallest prime in which the digit string can be partitioned in n+1 parts such that the product of the first n parts = the (n+1)th one.

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Extensions