A097957 -id:A097957 - cp's OEIS frontend

A002382 Numbers of the form (p^2 - 49)/120 where p is prime.

0, 1, 2, 4, 11, 15, 18, 23, 37, 44, 57, 78, 88, 95, 106, 134, 156, 205, 221, 232, 249, 310, 323, 414, 429, 452, 550, 576, 639, 667, 715, 785, 816, 837, 946, 1003, 1038, 1122, 1159, 1222, 1313, 1562, 1635, 1740, 1786, 1817, 1976, 2108, 2279, 2493, 2585, 2641

Offset: 1

N. J. A. Sloane

nonn

Primes p corresponding to a(n) are found in A003631(n+2) = A042993(n+3) = A097957(n+1). - Ray Chandler, Jul 29 2019

H. Gupta, On a conjecture of Chowla, Proc. Indian Acad. Sci., 5A (1937), 381-384.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
H. Gupta, On a conjecture of Chowla, Proc. Indian Acad. Sci., 5A (1937), 381-384. [Annotated scanned copy]

Cf. A002381, A002855, A003631, A042993, A097957.

Select[(Prime[Range[150]]^2-49)/120,IntegerQ] (* Harvey P. Dale, Jan 19 2014 *)

More terms from James Sellers, May 03 2000

A331029 Least integer of each composite prime signature where primes ending in 1 or 9 are treated distinctly from those ending in 3 or 7.

Original entry on oeis.org

1, 3, 9, 11, 21, 27, 33, 63, 81, 99, 121, 189, 209, 231, 243, 273, 297, 363, 441, 567, 627, 693, 729, 819, 891, 1089, 1323, 1331, 1701, 1881, 2079, 2187, 2299, 2457, 2541, 2673, 3003, 3267, 3969, 3993, 4389, 4641, 4851, 5103, 5643, 5733, 6061, 6237, 6561, 6897

Offset: 1

Andrew Howroyd, Jan 07 2020

This sequence is analogous to A025487. The two primes 2 and 5 are ignored and the remainder are divided into two distinct classes depending on the final digit of the prime. A combined prime signature is then created from the prime signatures of the two classes of prime.
Consider the problem of finding the smallest number having n divisors ending with 1 or 9 (sequence A085645). Solutions must lie in this sequence since numbers with the same composite prime signature as defined here will have the same number of divisors ending with 1 or 9.
Primes ending in either 1 or 9 are 11, 19, 29, 31, 41, 59, ... (A045468).
Primes ending in either 3 or 7 are 3, 7, 13, 17, 23, 37, ... (A097957).
The partial products of these two sequences form two sequences analogous to the primorial numbers (11, 11*19, 11*19*29, ... and 3, 3*7, 3*7*13, ...). In the same manner that A025487 can be defined as products of primorial numbers, an alternative description of this sequence is that it is the set of all products of the two primorial analogs.

			Primes in this sequence are 3 and 11 because these are the smallest primes in the two classes.
Semiprimes in this sequence are 9 = 3^2, 21 = 3*7, 33 = 3*11, 121 = 11^2,  209 = 11*19 because 3, 7 are the smallest primes ending with either 3 or 7 and 11, 19 are the smallest primes ending with either 1 or 9.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A025487, A045468 (primes ending in 1 or 9), A085645, A097957 (primes ending in 3 or 7), A331082.

GenS(lim, pred)={my(L=List(), S=[1]); forprime(p=2, oo, if(pred(p), listput(L,S); my(pp=vector(logint(lim, p), i, p^i)); S=concat([k*pp[1..min(if(k>1, my(f=factor(k)[,2]); f[#f], oo), logint(lim\k, p))] | k<-S]); if(!#S, return(Set(concat(L)))) ))}
Merge(s1, s2, lim)={Set(concat(vector(#s1, i, [t | t<-s1[i]*s2, t<=lim])))}
lista331029(lim)={Merge(GenS(lim, k->abs(k%10-5)==2), GenS(lim, k->abs(k%10-5)==4), lim)}
{ lista331029(10^4) }

cp's OEIS Frontend

A002382 Numbers of the form (p^2 - 49)/120 where p is prime.

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