A067377 -id:A067377 - cp's OEIS frontend

A133372 Semiprimes expressible as the sum of (at least two) consecutive semiprimes in at least 1 way.

10, 15, 25, 33, 39, 51, 58, 69, 77, 82, 85, 91, 93, 94, 95, 106, 115, 118, 122, 123, 133, 134, 142, 143, 146, 155, 158, 159, 161, 166, 177, 178, 185, 187, 201, 205, 209, 213, 215, 217, 219, 221, 226, 235, 237, 249, 253, 254, 262, 267, 274, 278, 291, 295, 298

Offset: 1

Jonathan Vos Post, Dec 21 2007

This is to A067377 as A001358 is to A000040.

			a(1) = 10 = 4 + 6 = 2 * 5.
a(2) = 15 = 6 + 9 = 3 * 5.
a(3) = 25 = 6 + 9 + 10 = 5^2.

Cf. A001358, A067377, A135363.

A001358 INTERSECTION A135363.

More terms from R. J. Mathar, Jan 13 2008

A336581 Mersenne exponents whose corresponding prime can be expressed as the sum of at least two consecutive primes.

Original entry on oeis.org

5, 7, 13, 17, 61

Offset: 1

Michel Marcus, Aug 30 2020

127 is a term.

			5 is a term because 2^5-1 = 7 + 11 + 13.
17 is a term because 2^17-1 = 43669 + 43691 + 43711.

Carlos Rivera, Puzzle 456. Mersenne Primes as a sum of consecutive primes, The Prime Puzzles and Problems Connection.

Cf. A000043 (Mersenne exponents), A000668, A050936, A067377.

isok(m) = my(p=2^m-1); isprime(p) && isA050936(p);

A350335 Primes expressible as the sum of (at least two) consecutive primes in at least 7 ways.

Original entry on oeis.org

3634531, 27411611, 28127521, 28445689, 48205429, 54604973, 56857523, 63461429, 70734089, 72087167, 75489781, 82183951, 83020733, 89752433, 92712023, 94026311, 100925263, 111282419, 137392361, 163506407, 164711999, 194039771, 195327179, 196364899, 196876789

Offset: 1

Jon E. Schoenfield, Dec 25 2021

nonn

Subsequence of A350334.

			3634531 is a term because it is a prime and
   3634531 = Sum_{j=42997..43003} prime(j)
           = Sum_{j=15749..15769} prime(j)
           = Sum_{j=7294..7342} prime(j)
           = Sum_{j=7032..7082} prime(j)
           = Sum_{j=3397..3509} prime(j)
           = Sum_{j=165..1003} prime(j)
           = Sum_{j=65..995} prime(j).

Cf. A067377, A067378, A067379, A067380, A067381, A164556, A350334.

cp's OEIS Frontend

A133372 Semiprimes expressible as the sum of (at least two) consecutive semiprimes in at least 1 way.

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A336581 Mersenne exponents whose corresponding prime can be expressed as the sum of at least two consecutive primes.

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A350335 Primes expressible as the sum of (at least two) consecutive primes in at least 7 ways.

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